Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 1

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 2

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 3

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 4

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 5

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 6

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 7

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 8

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 9

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 10

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 11

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 12

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 13

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 14

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 15

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 16

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 17

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 18

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 19

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 20

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 21

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 22

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 23

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 24

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 25

6-1 Using the Percent Proportion

Use the percent proportion to solve each problem.1. 18 is what percent of 72?

SOLUTION:  

So, 18 is 25% of 72.

2. What percent of 8 is 20?

SOLUTION:  

So, 250% of 8 is 20.

3. What is 74% of 56?

SOLUTION:  

So, 41.44 is 74% of 56.

4. 9 is 20% of what number?

SOLUTION:  

So, 9 is 20% of 45.

5. What percent of 2 is 8?

SOLUTION:  

So, 400% of 2 is 8.

6. Find 6% of 300.

SOLUTION:  

So, 18 is 6% of 300.

7. Find 9% of 255.

SOLUTION:  

So, 22.95 is 9% of 255.

8. Find 97% of 900.

SOLUTION:  

So, 873 is 97% of 900.

9. 16 is 80% of what number?

SOLUTION:  

So, 16 is 80% of 20.

10. 18 is 5% of what number?

SOLUTION:  

So, 18 is 5% of 360.

11. Of the 120 math tests, 47 were Bs. To the nearest tenth, what percent of the math tests were Bs?

SOLUTION:  Compare the number of B’s, 47, to the total number of math tests, 120. Let p represent the percent.

39.2% of the math tests were B’s.

12. An Aztec Salad gets 28 of its Calories from protein. If this is 20% of the total number of Calories, how many Calories does the salad have?

SOLUTION:  The percent is 20%, and the part is 78 Calories from protein. Let b represent the total number of Calories.

The salad has a total of 140 Calories.

Use the percent proportion to solve each problem.13. 4% of what number is 10?

SOLUTION:  

So, 4% of 250 is 10.

14. 55% of what number is 22?

SOLUTION:  

So, 55% of 40 is 22.

15. 21 is what percent of 50?

SOLUTION:  

So, 21 is 42% of 50.

16. 16 is what percent of 64?

SOLUTION:  

So, 16 is 25% of 64.

17. What percent of 145 is 52.2?

SOLUTION:  

So, 36% of 145 is 52.2.

18. What percent of 36 is 19.8?

SOLUTION:  

So, 55% of 36 is 19.8.

19. What is 60% of 120?

SOLUTION:  

So, 72 is 60% of 120.

20. What is 80% of 125?

SOLUTION:  

So, 100 is 80% of 125.

21. Find 65% of 440.

SOLUTION:  

So, 286 is 65% of 440.

22. Find 83% of 200.

SOLUTION:  

So, 166 is 83% of 200.

23. 12 is 40% of what number?

SOLUTION:  

So, 12 is 40% of 30.

24. 34 is 20% of what number?

SOLUTION:  

So, 34 is 20% of 170.

25. 80% of what number is 12?

SOLUTION:  

So, 20% of 15 is 12.

26. 4% of what number is 15?

SOLUTION:  

So, 4% of 375 is 15.

27. Sixteen of the 80 dogs at a kennel are golden retrievers. What percent of the dogs at the kennel are golden retrievers?

SOLUTION:  Compare the number of golden retrievers, 16, to the total number of dogs, 80. Let p represent the percent.

So, 20% of the dogs at the kennel are golden retrievers.

28. The number of lime-flavored gumballs in a gumball machine is 85. If this is 17% of the number of gumballs in the machine, how many gumballs are in the machine?

SOLUTION:  The percent is 17%, and the part is 85 lime-flavored gumballs. Let b represent the whole or the total number of gumballs.

There are 500 gumballs in the machine.

29. Use the circle graph that shows the results of a survey about New Year’s Resolutions. a. Determine about how many of the 2947 people surveyed said their most important New Year’s resolution was to get organized. b. About how many said their most important New Year’s resolution was to do more reading or to declutter?  

SOLUTION:  a.

About 973 people said their most important New Year’s resolution was to get organized. b.

About 766 people said their most important New Year’s resolution was to do more reading or to declutter.

30. Financial Literacy Accessories Central is having a summer clearance on sunglasses. Maria wants to buy a pair of sunglasses that cost $48 with a 65% discount. The same pair of sunglasses costs $38 with a 55% discount at Shades Inc. Which store has the better price for the pair of sunglasses? Explain your reasoning.

SOLUTION:  Accessories Central:

$48 − $31.20 = $16.80   Shades Inc.:

$38 − $20.90 = $17.10   Accessories Central has the better price for the pair of sunglasses because $16.80 < $17.10.

31. Identify Repeated Reasoning A pattern of equations is shown. 2% of 100 = 2 4% of 50 = 2 8% of 25 = 2 16% of 12.5 = 2 a. Describe the pattern. b. Find the next equation in the pattern.

SOLUTION:  a. The percent is increased by 2 and the whole is halved. Each answer is 2.b. 16% • 2% = 32% 12.5 ÷ 2 = 6.25   32% of 6.25 = 2

32. The bar graph shows the results of an online survey of 1242 people aged 15–25 about their political involvement overthe last 12 months. a. What percent of the people boycotted? Round to the nearest percent. b. Of the people who signed an e-mail petition, 20% were 18-years old. How many 18-year-olds signed an e-mail petition? c. Based on the results of the survey, predict about how many people out of 2000 would contact an official.  

SOLUTION:  a.

About 40% of the people boycotted. b.

Fifty-three 18-year olds signed an e-mail petition. c. Compare the number of people that contacted an official, 182, to the total number of people, 1242. Let p represent the percent.  

The percent is 14.65, and the base is 2000. Let a represent the part.

About 293 people would contact an official.

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary.33. 45 is what percent of 15?

SOLUTION:  

So, 45 is 300% of 15.

34. 13 is 25% of what number?

SOLUTION:  

So, 13 is 25% of 52.

35. What is 58% of 7?

SOLUTION:  

So, 4.1 is 58% of 7.

36. 8 is what percent of 2000?

SOLUTION:  

So, 8 is 0.4% of 2000.

37. What is 0.6% of 360?

SOLUTION:  

So, 2.2 is 0.6% of 360.

38. 41 is 5 % of what number?

SOLUTION:  

So, 41 is 5 % of 768.8.

39. The table shows the results of a student survey.

a. What percent of the students surveyed said their favorite act was playing instruments? b. If 10 more students vote for stand-up comedy, will the percent be greater than, less than, or equal to the current percent? Explain.

SOLUTION:  a. The total number of students surveyed is 198 + 150 + 212 + 80 = 640.

12.5% of students surveyed said their favorite act was playing instruments.b. Current percent:

  Add 10 to 198 and add 10 to 640 to calculate the new percent.

  The new percent, 32%, will be greater than the current percent of 30.9%.

40. Use the Internet or another source to find the percent of states that begin with A, I , O, or U.

SOLUTION:  There are 12 states that begin with A, I, O, or U (Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Ohio, Oklahoma, Oregon, and Utah).

24% of the 50 states begin with A, I , O, or U.

41. A cell phone store has 120 cell phones in stock. Of these, 45 have keyboards. The manager of the store wants to add more cell phones with keyboards so that 40% of the stock has keyboards. a. Write and solve a proportion to find the number of cell phones with keyboards that should be added to the store’s inventory. b. What will be the total number of cell phones in stock?

SOLUTION:  

a.

 

b.  The total number of cell phones in stock is 120 + 5 =125.

42. Model with Mathematics Write and solve a real-world problem involving percents.

SOLUTION:  Sample answer: A girl scout sold 108 boxes of cookies. Of the boxes sold, 27 were peanut butter cookies. What percent of the cookies sold were peanut butter?

25% of the cookies sold were peanut butter.

43. Persevere with Problems Without calculating, arrange the following from least to greatest value. Justify your reasoning.

25% of 160, 5% of 80, 25% of 80

SOLUTION:  5% of 80, 25% of 80, 25% of 160; If the percent is the same but the whole is the greater, then the part is greater. If the whole is the same but the percent is greater, then the part is greater.

44. Justify Conclusions Sabrina spelled 82% of her spelling words correctly on her spelling tests this year. If she spells13 out of 15 words correctly on her next test, will this help or hurt her average? Explain.

SOLUTION:  

Sample answer: This will help her average because ≈ 87% and 87% > 82%.

45. Persevere with Problems Find the value of y so that .

SOLUTION:  

46. Find the Error Bethany is finding what percent of 32 is 18. Find her mistake and correct it.

SOLUTION:  Her statement is incorrect. It should state that 18 is about 56% of 32. 

47. Make a Conjecture Is x% of y and y% of x always, sometimes, or never equivalent? Explain your reasoning.

SOLUTION:  

Always; sample answer: To find x% of y , solve for n. So, . To find  y% of x, solve for n.

So, .

48. Building on the Essential Question Kenji states that 5.9 is 125% of 47. Is his answer reasonable? Explain your reasoning.

SOLUTION:  Sample answer: His answer is not reasonable because 125% > 100% and 100% of 47 is 47. So, 125% must be greater than 47 and 5.9 < 47.

49. The table shows the results of a survey of middle school students about their favorite school mascots.

Based on the data, predict how many out of 2000 students would vote for the falcon.

 

A  600B  400C  300D  200

SOLUTION:  The total number of students surveyed is 60 + 123 + 86 + 131 = 400.   Compare the number of students that voted for the falcon, 60, to the total number of students, 400. Let p represent the percent.

The percent is 15, and the base is 2000. Let a represent the part.

Based on the data, predict that 300 students would vote for the falcon. Choice C is correct.

50. SHORT RESPONSE If 68 is 25% of a number, what is 600% of the number?

SOLUTION:  

68 is 25% of 272.  

1632 is 600% of 272.

51. A place kicker expects to make 75% of his field goal attempts this season. If he attempts 36 field goals this season, which of the following statements does not represent the place kicker’s expectation?

 

F  The place kicker will make 27 field goals.

G  The place kicker will miss 9 field goals.

H Less than  of the field goal attempts will 

be missed.

J The place kicker will make more than

 of his field goal attempts.

SOLUTION:  

75% of 36 is 27. The place kicker expects he that will make 27 field goals.   36 − 27 = 9 The place kicker expects that he will miss 9 field goals.  

 and 

The place kicker does not expect that less than  of his field goal attempts will be missed.

 

 and 27 > 18.

The place kicker expects that he will make more than  of his field goal attempts. Choice H is the correct answer.

52. If 40% of a number is 32, what is 35% of the number?

 

A  8B  20C  24D  28

SOLUTION:  

  40% of 80 is 32.  

  35% of 80 is 28. Choice D is correct.

53. In a survey, 35% of those surveyed said that they get the news from their local television station while three-fifths said that they get the news from a daily newspaper. From which source do more people get their news?

SOLUTION:  

is equivalent to 60%.

60% > 35%, so more people get their news from a daily newspaper.

Write each percent as a fraction in simplest form.54. 45%

SOLUTION:  

55. 120%

SOLUTION:  

56. 0.5%

SOLUTION:  

57. 83 %

SOLUTION:  

58. In a drawing of a honeybee, the bee is 4.8 centimeters long. The actual size of the honeybee is 1.2 centimeters. What is the scale of the drawing?

SOLUTION:  Let x = the actual length of the bee.

So, the scale is 1 cm = 0.25 cm.

Find each sum or difference. Write in simplest form.

59. 

SOLUTION:  

60. 

SOLUTION:  

61. 

SOLUTION:  

62. 

SOLUTION:  

63. 

SOLUTION:  

64. 

SOLUTION:  

Find each product.

65. 

SOLUTION:  

66. 

SOLUTION:  

67. 

SOLUTION:  

68. 

SOLUTION:  

eSolutions Manual - Powered by Cognero Page 26

6-1 Using the Percent Proportion