6-5 Solving Percent Problems

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Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

6-5 Solving Percent Problems

Warm UpSolve.

1. 4x = 90

2. 8x = 96

3. 12x = 180

4. 26x = 182

22.5

12

157

6-5 Solving Percent Problems

Problem of the Day

Rearrange the digits in . What

fraction of the possible arrangements are true proportions?

26

= 13

13

6-5 Solving Percent Problems

MA.7.A.1.2 Solve percent problems, including problems involving discounts…[and] taxes…

Sunshine State Standards

6-5 Solving Percent Problems

Sloths may seem lazy, but their extremely slow movement helps to make them almost invisible to predators. Sloths sleep an average of 16.5 hours a day. To find out what percent of a 24-hour day 16.5 hours is, you can use a proportion or an equation.

6-5 Solving Percent Problems

Proportion Method Equation Method

n100

= 16.524

PartWhole

PartWhole

What percent of 24 is 16.5?

n · 24 = 100 · 16.5

24n = 1,650

n = 68.75

n · 24 = 16.5

n = 0.6875

n = 68.75%

Sloths spend about 69% of the day sleeping!

6-5 Solving Percent Problems

Solve.

Additional Example 1A: Using Proportions to Solve Problems with Percents

What percent of 40 is 25?n

100= 25

40

n · 40 = 100 · 25

40n = 2,500

40n40

= 2,500 40

n = 62.5

25 is 62.5% of 40.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 40 to isolatethe variable.

6-5 Solving Percent Problems

Solve.

Additional Example 1B: Using Proportions to Solve Problems with Percents

15 is 25% of what number?

25100

= 15n

n · 25 = 100 · 15

25n = 1,500

25n25

= 1,500 25

n = 60

15 is 25% of 60.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 25 to isolatethe variable.

6-5 Solving Percent Problems

Solve.

Check It Out: Example 1A

What percent of 50 is 10?n

100= 10

50

n · 50 = 100 · 10

50n = 1,000

50n50

= 1,000 50

n = 20

10 is 20% of 50.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 50 to isolatethe variable.

6-5 Solving Percent Problems

Solve.

Check It Out: Example 1B

8 is 40% of what number?

40100

= 8n

n · 40 = 100 · 8

40n = 800

40n40

= 800 40

n = 20

8 is 40% of 20.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 40 to isolatethe variable.

6-5 Solving Percent Problems

Solve.

Additional Example 2A: Using Equations to Solve Problems with Percents

35 is 28% of what number?

35 = 28% · n

35 = 0.28 · n

350.28

= 0.28 · n0.28

125 = n

35 is 28% of 125.

Write an equation.

Write 28% as a decimal.

Divide each side by 0.28 to isolate the variable.

6-5 Solving Percent Problems

Solve.

Additional Example 2B: Using Equations to Solve Problems with Percents

What percent of 9 is 18?

18 = n · 9

189

= n · 99

2 = n

200% = n

18 is 200% of 9.

Write an equation.Divide each side by 9 to isolate the variable.Write the decimal as a percent.

6-5 Solving Percent Problems

Solve.

Check It Out: Example 2A

36 is 24% of what number?

36 = 24% · n

36 = 0.24 · n

150 = n

36 is 24% of 150.

Write an equation.

Write 24% as a decimal.

Divide each side by 0.24 to isolate the variable.

360.24

= 0.24 · n0.24

6-5 Solving Percent Problems

Solve.

Check It Out: Example 2B

What percent of 6 is 36?

36 = n · 6

366

= n · 66

6 = n

600% = n

36 is 600% of 6.

Write an equation.Divide each side by 6 to isolate the variable.Write the decimal as a percent.

6-5 Solving Percent Problems

Raoul found a pair of shoes that were marked down to 80% of the original price. He had a coupon that gave him an additional $10 off the shoes. The sales tax rate was 6.5% and Raoul paid $5.46 in sales tax. What was the original price of the pair of shoes?

Additional Example 3: Consumer Application

Write a word sentence.

Work backward. Find the final price of the shoes.

6.5% of price is $5.46.

Write an equation.0.065 x = 5.46

Divide both sides by 0.065.

x = 84The price of the shoes with the coupon was $84.

6-5 Solving Percent Problems

Additional Example 3 Continued

Find the price of the shoes without the coupon.

84 + 10 = 94The price of the shoes was $94 after it was marked down to 80% of the original price. Find the original price.

Write a word sentence.80% of price is $94.

Write an equation.0.8 x = 94

Divide both sides by 0.8.

x = 117.5

The original price of the shoes was $117.50.

6-5 Solving Percent Problems

Livy found a comforter marked down to 50% of the original price. She had a coupon that gave her an additional $10 off her purchase. The sales tax rate was 8.25% and Livy paid $6.19 in sales tax. What was the original price of the comforter?

Check It Out: Example 3

Write a word sentence.

Work backward. Find the final price of the comforter.

8.25% of price is $6.19.

Write an equation.0.0825 x = 6.19

Divide both sides by 0.0825.

x = 75.03The price of the comforter with the coupon was $75.03.

6-5 Solving Percent Problems

Check It Out: Example 3 Continued

Find the price of the comforter without the coupon.

75.03 + 10 = 85.03

The price of the comforter was $85.03 after it was marked down to 50% of the original price. Find the original price.

Write a word sentence.50% of price is $85.03.

Write an equation.0.5 x = 85.03

Divide both sides by 0.5.

x = 170.06

The original price of the comforter was $170.06.

6-5 Solving Percent Problems

A portable DVD player costs $225 before tax at an appliance warehouse. What is the sales tax rate if the tax is $18?

Additional Example 4: Finding Sales Tax

n100

= 18225

n · 225 = 100 · 18

8% of $225 is $18. The sales tax is 8%.

Write a proportion.

Set the cross products equal.

Multiply.

Restate the question: What percent of $225 is $18?

225n = 1800

225n225

= 1800225

Divide each side by 225.

n = 8

6-5 Solving Percent Problems

A new flat screen TV costs $800 before tax at an appliance warehouse. What is the sales tax rate if the tax is $56?

Check It Out: Example 4

n100

= 56800

n · 800 = 100 · 56

7% of $800 is $56. The sales tax is 7%.

Write a proportion.

Set the cross products equal.

Multiply.

Restate the question: What percent of $800 is $56?

800n = 5600

800n800

= 5600 800

Divide each side by 800.

n = 7

6-5 Solving Percent Problems

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

6-5 Solving Percent Problems

Lesson QuizSolve.

1. 21 is 42% of what number?

2. What percent of 292 is 73?

3. 112% of what number is 84?

4. What percent of 1,340 is 13.4?

5. An ad features a bicycle on sale for $139. If the total cost of the bike is $147.34, what is the sales tax rate?

25%

50

75

1%

6%

6-5 Solving Percent Problems

1. Solve. 19 is 38% of what number?

A. 69

B. 50

C. 38

D. 34

Lesson Quiz for Student Response Systems

6-5 Solving Percent Problems

2. What percent of 170 is 51?

A. 25%

B. 30%

C. 40%

D. 50%

Lesson Quiz for Student Response Systems

6-5 Solving Percent Problems

3. 128% of what number is 96?

A. 25

B. 50

C. 75

D. 96

Lesson Quiz for Student Response Systems

6-5 Solving Percent Problems

4. What percent of 1,520 is 15.2?

A. 25%

B. 15%

C. 10%

D. 1%

Lesson Quiz for Student Response Systems

6-5 Solving Percent Problems

5. A jeweler has a pendant on sale for $150. If the total cost of the pendant is $160.50, what is the sales tax rate?

A. 6%

B. 7%

C. 8%

D. 9%

Lesson Quiz for Student Response Systems