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Reasoning with Equations

1. What is the difference between an expression and an equation?

2. Can you name 3 words that indicate each operation?

3. How do you evaluate an expression?

4. Explain how distribution can simplify a problem.

5. What are like terms?

6. How do you combine like terms?

7. What are inverse operations? Name them.

8. How do you solve equations?

9. What do you do when an equation has variables on both sides?

10. How do you transform equations? Why would you want to?

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Reasoning with Equations Chapter Problems

Vocabulary, Equations & Expressions

Classwork

1) Circle the constant and underline the coefficient for each expression below

a. 5x – 3

b. 2x + 7

c. 2 – 4x

d. x + 3

2) Create an algebraic expression with a coefficient of 7 and a constant of 4.

3) Create an algebraic expression with a coefficient of -1 and a constant of -12.

4) Create an equation that contains a coefficient of 6.

5) Create an equation that contains a coefficient of -13.

6) What is the difference between an algebraic expression and an equation?

7) Which are algebraic expressions?

5x – 2 8x w 14 + 5x 2w – 6 4x – 8 = 9

Homework

8) Circle the constant and underline the coefficient for each expression below

a. 3x – 5

b. 2x - 1

c. 7 – 8x

d. x + 2

9) Create an algebraic expression with a coefficient of 17 and a constant of 3.

10) Create an algebraic expression with a coefficient of -1 and a constant of -1.

11) Create an equation that contains a coefficient of 4.

12) Create an equation that contains a constant of -12.

13) What is the difference between an algebraic expression and an equation?

14) Which are algebraic expressions?

17m 8 – 3z w 9w + 4 = 12 12 + 7t 6y + 4


Translating between Words & Expressions

Classwork

Translate the words into an algebraic expression.

15) 4 times x

16) The sum of x and 6

17) The product of 9 and y

18) w less than 8

19) 5 more than x

20) The difference of 6 and x

21) 9 times the sum of x and 4

22) The product of 5 and y divided by 3

23) The quotient of 300 and the quantity of x times 2

24) x less than 32

25) The quotient of 35 and the quantity of x minus 7

26) The product of 7 and x minus the quantity of 4 less than y

27) The quantity of 9 more than x divided by the quantity of 12 less than y

Homework

Translate the words into an algebraic expression.

28) The product of 14 and x

29) The quotient of x and 5

30) The sum of 19 and w

31) w less than 8

32) 7 less than x

33) The difference of 16 and y

34) 9 times the quotient of x and 20

35) The product of 6 and x less 3

36) The quotient of 100 and the sum of x and 2

37) x less than 2

38) The product of 5 and the quantity of x less than 7

39) The product of 27 and y divided by the quantity of 4 more than y

40) The quantity of 6 less than x divided by the quantity of 2 more than y


Tables & Expressions

Classwork

Complete the table.

41)

42)

43)

44)

45)

46)


n 3n 51015

n n + 7 3 57n n - 70 80100120140

n n ÷ 801816

n 4 less than n20181614

n 2 more than n20181614

47) Adult ticket prices are $3 more than child ticket prices. Determine the adult ticket price, given the child ticket price.

Child Ticket Price Adult Ticket Price$5$7$10$12

48) Write an expression that represents the adult price, if the child price is “x”

49) For NJASK testing, 25 students are placed in each classroom. Determine the number of classrooms needed, given the number of students testing.

50) Write an expression that represents the number of classrooms needed, if the number of students testing is “x”

51) Mary has ½ the amount of money that Jim has. Determine the amount of money that Mary has, given Jim’s amount of money.

52) Write an expression that represents the amount of money Mary has, given the amount of Jim’s

money.

53) Each person running in the race paid $20. Determine the amount of money collected, given the amount of people running in the race.

54) Write an expression that represents the amount of money collected, given the number of people running in the race.


Number of Students Testing Number of Classroom Needed250325400520

Jim’s amount of money Mary’s amount of money$50$100$175$220

Number of People Running Amount of Money Collected150230410520

55) A car is traveling at 60 mph for 4 hours then decreases speed to 45 mph for 2 more hours. a) Fill out the table to model the situation.

Hour Miles traveled123456

b) How many miles did the car travel?

c) If the car gets 22 miles per gallon, how many gallons of gas did you use?

Write an expression for the following situations.

56) Bob weighs 7 more pounds than Jack. Jack weighs x pounds. Bob’s weight:

57) Tiffany has 6 dollars less than Jessica. Jessica has x dollars. Tiffany’s money:

58) Samantha has 12 more stickers than Mike. Mike has S stickers. Samantha’s sticker amount:

59) The recipe calls for twice the amount of sugar than flour. There is F amount of flour in the recipe. Amount of sugar:

60) Mark’s quiz grade is one more than twice Ted’s quiz grade. Ted’s quiz grade is x. Mark’s quiz grade:

61) Laura paid x dollars for her prom dress. Beth paid four dollars less than Laura. Beth’s prom gown price:

62) David ran the 5k in x minutes. Harry ran the same race in five minutes less than double David’s time. Harry’s time:

63) The beans grew K inches. The tomatoes grew 3 inches more than triple the height of the beans. Tomato height:

Create a scenario for the following expressions:

64) x + 5

65) 2(x – 3)

Homework

Complete the table.

66)


n 5 + n 51015

67)

68)

69)

70)

71)

72) Child ticket prices are $3 less than adult ticket prices. Determine the child ticket price, given the adult ticket price.

Adult Ticket Price Child Ticket Price$10$15$20$25

73) Write an expression that represents the child price, if the adult price is “x”


n 7n 3 57

n n 10

80100120140

n n ÷ 201816

n 34 less n20181614

n 5 less than n20181614

74) For bussing, 40 students are assigned to each bus. Determine the number of busses needed, given the number of students riding.

Number of Students Riding Number of Busses Needed240320400500

75) Write an expression that represents the number of busses needed, if the number of students riding is “x”

76) The farm always has four times the number of chicks as hens. Determine the number of chicks, given the number of hens.

Number of hens Number of chicks20405060

77) Write an expression that represents the number of chicks, given the number of hens.

78) Each person running in the race will eat two hotdogs. Determine the number of hotdogs needed, given the amount of people running in the race.

Number of People Running Number of Hotdogs needed150230410520

79) Write an expression that represents the number of hotdogs needed, given the number of people running in the race.


80) A car is traveling at 75 mph for 4 hours then decreases speed to 55 mph for 2 more hours. a) Fill out the table to model the situation.

Hour Miles traveled123456

b) How many miles did the car travel?

c) If the car gets 22 miles per gallon, how many gallons of gas did you use?

Write an expression for the following situations.

81) Bob weighs 17 pounds less than Jack. Jack weighs x pounds. Bob’s weight:

82) Tiffany has 50 dollars more than Jessica. Jessica has x dollars. Tiffany’s money:

83) Samantha has 12 times as many stickers than Mike. Mike has S stickers. Samantha’s sticker amount:

84) The recipe calls for triple the amount of sugar than flour. There is F amount of flour in the recipe.

Amount of sugar:

85) Mark’s quiz grade is six more than double Ted’s quiz grade. Ted’s quiz grade is x. Mark’s quiz grade:

86) Laura paid x dollars for her prom dress. Beth paid 16 dollars more than Laura.

Beth’s prom gown price:

87) David ran the 5k in x minutes. Harry ran the same race in half the time that David ran the race.

Harry’s time:

88) The beans grew K inches. The tomatoes grew triple the height of the beans less 2 inches. Tomato

height:

Create a scenario for the following expressions:

89) 2(x + 3)

90) x - 4

Evaluating Expressions

Classwork

Evaluate the expression for the given value

91) (2n + 1)2 for n = 392) 2(n + 1)2 for n = 493) 2n + 22 for n = 394) 4x + 3x for x = 595) 3(x – 3) for x = 7


96) 8(x + 5)(x – 2) for x = 497) 3x2 for x = 298) 5x + 45 for x = 6

99)4 x5

for x = 10

100) 4y + x for x = 2 and y = 3

101)xy+17 for x = 12 and y = ½

102) 6x + 8y for x = 9 and y = ¼103) x + (2x – 8) for x = 10104) 5(3x) + 8y for x = 2 and y = 10

Use the distance formula, D = rt, to find the distance traveled

105) Rate: 40 mph; Time: 2 hrs106) Rate: 60 mph; Time: 5 hrs107) Rate: 34 mph; Time: ½ hr

108) Riding downhill on your bike you accelerate from 6 m/s to 10 m/s over 7 seconds. What is your acceleration?

a=(v−v0)t

Homework

Evaluate the expression for the given value

109) (2n + 1)2 for n = 1110) 2(n + 1)2 for n = 3111) 2n + 22 for n = 5112) 4x + 3x for x = 6113) 3(x – 3) for x = 3114) 8(x + 5)(x – 2) for x = 6115) 3x2 for x = 8116) 5x + 45 for x = 3

117)4 x5 for x = 15

118) 4y + x for x = 12 and y = 13

119)xy+17for x = 2 and y = ½

120) 6x + 8y for x = 8 and y = ¾121) x + (2x – 8) for x = 11122) 5(3x) + 8y for x = 12 and y = 5

Use the distance formula, D = rt, to find the distance traveled

123) Rate: 14 mph; Time: 2 hrs124) Rate: 60 mph; Time: ¾ hrs125) Rate: 40 mph; Time: ½ hr

126) Climbing a mountain pass on your bike you decelerate from 6 m/s to 3 m/s over 45 seconds. What is your acceleration?


a=(v−v0)t

Distributive Property

Classwork

Use the Distributive Property to rewrite the expressions without parentheses

127) (x + 4)128) 8(x – 2)129) 6(x + 4)130) -1(x – 4)131) (x + 2)8

Homework

Use the Distributive Property to rewrite the expressions without parentheses

132) 5(x + 4)133) 7(x – 12)134) 3(x - 14)135) -1(x – 2)136) (x - 2)5Like Terms

Classwork

Create a like term for the given term.137) 4x138) 13y139) 15x2

140) 16xy141) x

Homework

Create a like term for the given term.142) 6x143) Y144) 10x2

145) 14xy146) -5x

Combining Like Terms

Classwork

Simplify the expression if possible.

147) 7x + 8x148) 6x + 8y + 2x


149) 15x2 + 5x2

150) 5x +2(x + 8)151) -10y + 4y 152) 9(x + 5) + 7(x – 3)153) 8 + (x – 4)2154) 7y + 8x + 3y + 2x155) x + 2x156) x2 + 5x2

157) 2x + 4x + 3158) 6y – 3y159) 9y + 4y – 2y + y160) x + 5x + x + 12161) 8x – 3x + 2x + 15

Homework

Simplify the expression if possible.

162) 17x + 18x + 3163) 6x + 8y - 2x – y164) 15x2 + 5x2 + 2x165) 5x +2(x + 8) + 3166) -10y + 4y – 5167) 9(x - 5) + 7(x + 3)168) 18 + (x – 4)2 – 4169) 7y + 8x + 3y + 2x + 9170) x + 2x + x + 5x171) 6x2 + 5x2

172) 12x + 14x + 3y173) 6y – 3y + 6xy + 4xy174) 9y + 4y – 2y + y + y2

175) x + 5x + x + 12 – 7x176) 8x – 3x + 2x + 15 – 7y

Inverse Operations

Classwork

177) Name the inverse operation needed to solve for the variable.

a. x + 9 = 17

b. y – 8 = 5

c. m + 5 = 21

d.

w6

=12

e. 9v = 108

Homework


178) Name the inverse operation needed to solve for the variable.

a. t – 18 = 54

b. 14x = 228

c. m + 19 = 51

d. 11b = 66

e.

m4=2

One Step Equations

Classwork

Solve.

179) n + 7 = 20180) x + 9 = -8181) a – 15 = 27182) y – 21 = -15183) 50 + w = 92184) -4 + m = 18

185)

m8=16

186) 30 = 12m187) -5m = 25

188)

16t=12

189) -10c = -80190) n – (-6)= 12191) -82 + x = -20

192)

−r2

=5

Homework

Solve.

193) n + 9 = 13194) -14 + b = 21195) z – 18 = -14196) -7 + g = -12197) 19 = 15 + y198) b + (-4) = 13


199)

q3=33

200) -18x = -360201) x – 11 = 4

202)

15n=15

203) -15c = -75204) -8 + r = 27205) 19 + m = 3

206)

−w8

=1

Two Step Equations

Classwork

Solve.

207) 7x – 2 = 26

208) ½ (m – 3) = 12

209) -6h – 6 = 30

210) 5x + 20 = -20

211) 3 = -3y – 15

212) -24 = 14y – 5

213) 7r – 5 = 10

214) 9 = 16y + 51

215) 13x + 6 = 6

216)

x−4

+11=5

Homework

217) 2m – 8 = -28

218)

x9−3=8


219) 12m + 20 = -40

220)

−x3

+5=21

221) 8r – 27 = -19

222)6+ k3=33

223) 15 = -4y – 9

224) 8w + 4 = -36

225) 4a – 15 = -23

226) 44 = 5x - 6

Multi-Step Equations

Classwork

Solve.

227) 8s – (8 + 6s) = 20

228) 34 = 2x + 8(x + 3)

229)

34( x+9 )=15

230)

23(m−8)=4

231) 35 = 22x – 12x + 5

232) 6(b + 8) = 54

233) 99 = 33x + 3(3x + 5)


234) –t + (5t – 7) = -5

235) 21 – 3(2 – w) = -12

236) 9 = 8b – (2b – 3)

Homework

Solve.

237) 6(m + 4) – 2m = -8

238) 44 = 4(8 + h)

239)

34(8 t−4 )=−2

240)0=15(10h+15 )+h

241) 3(5 – t) – 4t = 18

242) 2(y - 5) = 16

243) 0.1(h + 20) = 3

244)

3 z8

−4=5

245) 8.6 = 6j + 4j

246) 12z – (4z + 6) = 82

Variables on Both Sides

Classwork

Solve.


247) 18 – 5t = t

248) 3m – 6 = 5m + 8

249) 22w – 42 = 34 – 16w

250) r + 6 – 5r = 14 – 2r

251) 6x + 12 = 4x

252) 4n – 14 = -16n + 26

253) y – 2y + 3 = 3 – y

254) 4u – 7 = u + 3(4 + u)

255) 4m – (8 – m) = 6 – 2m

256) 3b + 16 = 5b + 16 – 2b

Homework

Solve.

257) 2m = 24 + 3m

258) 5w – 17 = 12 – 5w

259) 2p – 9 = 5p + 12

260) 35 – y = 4y

261) 10x = 4x – 8x + 7

262) 2s + 16 = s – 25

263) 14 – (2c + 5) = -2c + 9

264) 20 – 16p = 4(5 – 4p)

265) 4n + 8 = 8 – 4n

266) 1.4h = 1.8h + 4.8 – 0.4h

More Equations

Classwork


267)

16(6w−12)=6−2(w−2 )

268) 6(6 – 2a) = -27a -

32 (-4a + 6)

269) 2b + 4(b – 6) = -2(2b – 14) + 98

270) 4g + 3(g – 2) = -5(g – 4) – g

271) -7 + 8(5 – 3s) = 3(7 – 9s)

272) The sum of the ages of the three Romano brothers is 63. If their ages can be represented as consecutive integers, what is the age of the middle brother?1

Homework

273)

23( 9x−15)=17−3( x−12 )

274) 2(3x – 4) = -2x + 40275) 3(1 + 2x) – 4x = -(x + 30)276) 8g + 6(g – 2) = -10(g – 4) – 2g277) 12(3n – 7) + 8n = -2(4 – 3n)278) Arielle has a collection of grasshoppers and crickets. She has 561 insects in all. The number of

grasshoppers is twice the number of crickets. Find the number of each type of insect that she has2.

Literal Equations

Classwork

279) Solve for w. A = lw

280) Solve for m. t= v+m

3

281) Solve for b. 16c−10b=2

282) Solve for h. A=1

2bh

1 From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.2 From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.


283) Solve for π . V= 4

3πr3

Homework

284) Solve for l. P = 2l + 2w

285) Solve for c. p=b+c

5

286) Solve for s. 20 x−5 s=8

287) Solve for h. V=2πr2h

288) Solve for h.

289) The formula for the volume of a right circular cylinder is V = πr2h.

The value of h can be expressed as3

a.Vπr2

b.Vπ r2

c. π r2

Vd. V−π r2

290) If c = 2m + d, then m is equal to4

a) c−d2

b)c2−d

c) c−d2d) d−2

3 From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.4 From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.


A=12(b1+b2 )h

Unit Review

Reasoning with Equations Multiple Choice Questions

1. 3x and -2xa. Are Like Termsb. Are Unlike Terms

2. 5a and 5ba. Are Like Termsb. Are Unlike Terms

3. 4y and 5xya. Are Like Termsb. Are Unlike Terms

4. x2y and xy2

a. Are Like Termsb. Are Unlike Terms

5. 22 and 14a. Are Like Termsb. Are Unlike Terms

6. xy and –xya. Are Like Termsb. Are Unlike Terms

7. Match the expression 3(-4 + 3) with an equivalent expression. a. 4(3) + 4(3)b. 3(-4) + 3(3)c. 4(3) - 4(3)d. 3(4) + 3(3)

8. Which algebraic expression represents the number of days in w weeks? a. w – 7b. w/7c. w + 7d. 7w


9. Which algebraic expression represents the number of hours in m minutes? a. m – 60b. m/60c. m + 60d. 60m

10. In the expression 3x + 5, the value of 3 best describes:a. the constantb. the operationc. the variabled. the coefficient

11. In the expression 2x + 16, the value of 16 best describes:a. the coefficientb. the variablec. the operationd. the constant

12. Evaluate the expression 2x, when x = 10a. 20b. 12c. 210

d.

13. What operation is being performed between the number and variable in the expression

?a. additionb. divisionc. subtractiond. multiplication

14. A group of 15 parents buys tickets to a fundraiser show and receives a group discount of $2 off the regular ticket price p. Which expression represents the total cost of the tickets, in dollars?a. 15 • p + 2b. 15 • (p - 2)c. p - 15 • 2d. p • (15 - 2)


15. A music store sells CDs for $15 and tapes for $3. Which expression could be used to find the dollar total of the sales for an hour if the store sold 8 CDs and 5 tapes?a. (8 + 15) • (5 + 3)b. (8 •15) + (5 • 3)c. (8 • 3) + (5 •15)d. (15 ÷8) + (5 ÷ 3a)

16. There were three times as many adults as students attending a school play. If the attendance was 480, how many adults and how many students attended the play?a. 360 students, 120 adultsb. 240 students, 240 adultsc. 120 students, 360 adultsd. 160 students, 320 adults

17. Which of the following is not a variable expression? a. 4nb. n + mc. n - 4 d. 4 + 3

18. What is the value of the expression x + y when x = 15 and y = 21?a. 6b. 30c. 36 d. 42

19. Evaluate n2

- m when m = 7 and n = 8.a. 9b. -9c. 57 d. 71

20. Claire has had her driver’s license for three years. Bill has had his license for “b” fewer years than Claire. Which expression can be used to show the number of years Bill has had his driver’s license?a. 3 + bb. b + 3c. 3 - b d. b < 3


21. Which situation is best modeled by the expression 25 – x?a. George places “x” more video games on a shelf with 25 gamesb. Sarah has driven “x” miles of a 25 mile tripc. Ameilia paid $25 of an “x” dollar lunch she shared with Ariel d. George has 25 boxes full of “x” baseball cards each

22. Evaluate -3x + 5 when x = -2a. 11b. -1c. 1 d. -11

23. Nine decreased by the quantity eight times a number “x”.a. 8x - 9b. 9 – 8xc. 9x - 8 d. 8 – 9x

24. Four more than the quotient of 25 and y.

a.

b.

c.25+4y

d.y

25−4

25. What is the coefficient of x in the expression 4y + 5 - x?a. 5b. 1c. -1d. 0

26. Name the inverse operation used to solve this equation: x - 15 = -10a. Multiplicationb. Division


c. Additiond. Subtraction

27. Name the inverse operation used to solve this equation: 4s = 84a. Multiplicationb. Divisionc. Additiond. Subtraction

28. Name the inverse operation used to solve this equation: f/4 = 2 a. Multiplicationb. Divisionc. Additiond. Subtraction

29. Name the inverse operation used to solve this equation: -18 + x = 30 a. Multiplicationb. Divisionc. Additiond. Subtraction

30. Solve the equation: y + 17 = 29 a. y = 36b. y = 12c. y = -12d. y = 11

31. Solve the equation: 2 - 20x = 162a. x = -8.2 b. x = 8.2c. x = 8 d. x = -8

32. Solve the equation: 4.3d = -288.1a. d = -283.8 b. d = -292.4c. d = 67d. d = -67

33. Solve the equation: 4.0 + 8.7k - 2.6 = 2 a. k = 14.5 b. k = -14.5 c. k = 0.39d. k = 5.22

34. Solve the equation: 5/7r - 2 = -1


a. r = 7/5 b. r = 5/7 c. r = -4 1/5 d. r = -2 1/7

35. Solve the equation: 3/8 + 1/2w - 4 = 3 a. w = 13 1/4b. w = 1 13/14 c. w = 106/4 d. w = 13

36. Solve the equation: -3(2u + 5) + 3.5u = -1u a. u = 10b. u = -10c. u = 4d. u = -4

37. Solve the equation: -4a = 14a - 12(4a+ 10) a. a = 10b. a = 4 c. a = -4 d. a = -10

38. Solve the equation: 2(x + 6) = 2(-x + 6.5) a. x = 13 b. x = 0.4c. x = 4d. x = 1/4

39. Solve the equation: 5t = 2 - t a. t = -6b. t = -1/3c. t = 1/3 d. t = 6

Reasoning with Equations Short Constructed Response

40. A rectangle is 6 inches longer than it is wide. Write and simplify an expression for the perimeter of the rectangle in terms of the width w.

41. You and a friend worked in the school store last week. You worked 4 hours less than your friend. Let h be the number of hours your friend worked. Write an expression in simplest form that represents the total number of hours you both worked.


42. A trail mix contains peanuts, raisins, and M&Ms. In the mix, the amount of peanuts is three times the amount of M&Ms; and the amount of raisins is two times the amount of M&Ms. Let m represent the amount of M&Ms. Write and simplify an expression for the total number of pieces of food in the trail mix.

43. Write an expression containing three terms that is in simplest form. One of the terms should be constant.

44. Simplify: 5 – 2(3x – 4) + x

45. Shelly lives 500 miles away. Paul drove 65 mph for 4 hours. How many more miles will it take for him to arrive at Shelly’s house?

46. Evaluate the expression 59 (F – 32) when F = 41

47. 8x - 18 = 46 x =

48. 27.5 = 2.5q + 1q -4 q =

49. -3e + 8 = -1 e =

50. 2/5y + y - 8 = 11 y =

51. -14.5b - 3 + 0.5b = 18 b =


52. -6(2m +1) = 3m + 54 m =

53. 2x - 4 - 2x = -(8x + 2) x =

54. 3(2x + 3) = 2(x - 4) x =

55. -5( -10 +8v) = -30 v =

56. 1/6c + 0.5 + 5/6c = 1 c =

Reasoning with Equations Extended Constructed Response

57. At the video arcade, Jenny buys 25 tokens. She uses two tokens for each game she plays.Write an expression for the number of tokens Jenny has left after playing g games.

Find the number of tokens Jenny has left after playing 1, 4, 6, 10 and 12 games.

58. Bob wants to go to the movies with his friends. The movie theater charges $8 per ticket. Bob’s friends reserve $48.00 worth of tickets in advance. How many people in total can attend the movie?

Identify the variable

Identify the constant

Write an equation which includes the number of people attending the movie, the price of each ticket, and the total cost of the movie.

59. Write an expression that has four terms and simplifies to 16x + 5. Identify the like terms


Identify the coefficients

Identify the constant terms

Bob Mary

60. Mary is 5 years older than Bob. When Bob is 65, 70, and 75 years of age, what will Mary’s age be? Complete the chart with an expression containing a variable to explain your answer.

61. A cell phone company is offering 2 different monthly plans. Each plan charges a monthly fee plus an additional cost per minute.

Plan A: $ 40 fee plus $0.45 per minute

Plan B: $70 fee plus $0.35 per minute

a) Write an expression to represent the cost of Plan A

b) Write an expression to represent the cost of Plan B

c) Which plan would be least expensive for a total of 100 minutes?

62. Chad complained to his friend that he had five equations to solve for homework. Are all of the homework problems equations? Justify your answer.

Math Homework1. 3x2 ∙ 2x4

2. 5 – 2x = 3x

3. 3(2x + 7)

4. 7x2 + 2x – 3x2 – 9


5.23= x+26

63. The clerk at the bank desk says there is an initial charge of $50.00 to open up a bank account at the Sunny Farms Bank. He then explains that after, every account added on will cost an additional $15.50 each. The Smith Family is thinking of opening an account for the family.

a) Write an equation that represents the cost to open accounts for the family members.

b) What is the greatest amount of family members that could open a bank account without exceeding a fee of $500?

c) How much money would it cost if Mom Smith, Dad Smith, Sister Smith, and Brother Smith want to open an account, and Mom Smith has a special discount coupon of 15% off the final price?

64. The Rainbow Phone Service Company has a monthly fee of $100 and an additional charge of $6.00 for every data one goes over a month. The Cellular Phone Service Company has a monthly fee of $80 and an additional charge of $10.00 for every data one goes over. The Gomez family is deciding which of these two phone providers to subscribe to5.

a) Write an equation that represents the cost of each phone company’s monthly fee. Let p = cost.

b) For what number of data over will the total monthly fee for both companies be the same?

c) The Gomez family’s daughter went over 6 data last month. Which phone service will save the Gomez family the more if the daughter repeats this bad habit next month?

5 From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.


Answer Key1.

a. constant: -3, coefficient: 5b. constant: 7, coefficient: 2c. constant: 2, coefficient: -4d. constant: 3, coefficient: 1

2. 7x+43. –x-124. 6x+1, answers will vary5. -13x+1, answers will vary6. An algebraic expression is unsolvable and

does not contain an equal sign.7. 5x-2, 8x, w, 14+5x, 2w-68.

a. constant: -5, coefficient: 3b. constant: -1, coefficient: 2c. constant: 7, coefficient: -8d. constant: 2, coefficient: 1

9. 17x+310. –x-111. 4x+2, answers will vary12. -12x+2, answers will vary13. An algebraic expression is unsolvable and

does not contain an equal sign.14. 17m, 8-3z, w 12+7t, 6y+415. 4x

16. x+617. 9y18. 8-w19. 5+x20. 6-x21. 9(x+4)22. 5y/323. 300/2x24. 32-x25. 35/(x-7)26. 7x-(y-4)27. 9+(x/(y-12))28. 14x29. x/530. 19+w31. 8-w 32. x-733. 16-y34. 9x/2035. 6(3-x)36. 100/(x+2)37. 2-x38. 5(7-x)39. 27y/(4+y)40. (x-6)/(2+y)

41.

42.

43.

44.


n 3n 5 1510 3015 45

n n + 7 3

10

5

12

7 14

n n - 70 80 10100 30120 50140 70

n n ÷ 80 01 1/88 116 2

45.

46.

47. Child Ticket Price Adult Ticket Price$5 $8$7 $10$10 $13$12 $15

48. x+349.

50. x/25 51.

52. x/253.

54. 20x


n 4 less than n20 1618 1416 1214 10

n 2 more than n20 2218 2016 1814 16

Number of Students Testing Number of Classroom Needed250 10325 13400 16520 21

Jim’s amount of money Mary’s amount of money$50 $25$100 $50$175 $87.50$220 $110

Number of People Running Amount of Money Collected150 $3000230 $4600410 $8200520 $10400

55. A)

Hours Miles1 602 1203 1804 2405 2856 330

b) 330 mic) 15 gallons

56. x+757. x-658. s+1259. 2f60. 2x+1

61. x-462. 2x-563. 3k+364. Multiple Answers65. Multiple Answers

66.

67.

68.

69.


n 5+n 3

10

5

15

7 20n 7n3 215 357 49

n n 10

80 8100 10120 12140 14

n n ÷ 20 01 .58 416 8

70.

71.

72. Adult Ticket Price Child Ticket Price$10 $7$15 $12$20 $17$25 $22

73. x-374.

Number of Students Riding Number of Busses Needed240 6320 8400 10500 13

75. x/40 76.

Number of hens Number of chicks20 8040 16050 20060 240

77. 4x 78.

Number of People Running Number of Hotdogs needed150 300


n 34 less n20 1418 1616 1814 20

n 5 less than n20 1518 1316 1114 9

230 460410 820520 1040

79. 2x80. A)

Hour Miles1 752 1503 2254 3005 3556 410

b) 410 mic) 18.63 gallons

81. x-1782. 50+x83. 12S84. 3F85. 6+2x86. x+1687. x/288. 3(K-2)89. Multiple Answers90. Multiple Answers91. 4992. 5093. 1094. 3595. 1296. 14497. 1298. 7599. 8100. 14101. 41102. 56103. 22104. 110105. 80 mi106. 300 mi107. 17 mi108. 4/7 m/s2

109. 9110. 32111. 14112. 42113. 0114. 352115. 192116. 60117. 12118. 64119. 21120. 54

121. 25122. 220123. 28 mi124. 45 mi125. 20 mi126. 1/5 m/s2

127. x+4128. 8x-16129. 6x+24130. –x+4131. 8x+16132. 5x+20133. 7x-84134. 3x-42135. –x+2136. 5x-10137. Multiple Answers ex:2(2x)138. Multiple Answers ex:26y/2139. Multiple Answers ex:(3x)(5x)140. Multiple Answers (4x)(4y)141. Multiple Answers ex:x2/x142. Multiple Answers ex: 3(2x)143. Multiple Answers ex. 5y – 4y 144. Multiple Answers ex. 5x(2x)145. Multiple Answers ex. 7x(2y)146. Multiple Answers ex. 5x – 10x147. 15x 148. 8x+8y149. 20x2

150. 7x+16151. -6y152. 16x+24153. 2x154. 10y+10x155. 3x156. 6x2

157. 6x+3158. 3y159. 12y160. 7x+12


161. 7x+15162. 35x+3163. 4x+7y164. 20x2+2x165. 7x+19166. -6y-5167. 16x-24168. 2x+6169. 10y+10x+9170. 9x171. 11x2

172. 26x+3y173. 3y+10xy174. 12y+y2

175. 12176. 7x+15-7y177.

a. Subtractionb. Additionc. Subtractiond. Multiplicatione. Division

178. a. Additionb. Divisionc. Subtractiond. Divisione. Multiplication

179. 13180. -17181. 42182. 6183. 42184. 22185. 128186. 2.5187. -5188. 72189. 8190. 6191. 62192. -10 193. 4194. 35195. 4196. -5197. 4198. 17199. 99200. 20201. 15202. 75203. 5204. 35205. -16

206. -8207. 4208. 27209. -6210. -8211. -6212. -19/14213. 15/7214. -21/8215. 0216. 24217. -10218. 99219. -5220. -48221. 1222. 81223. -6224. -5225. -2226. 10227. 14228. 1229. 11230. 14231. 3232. 1233. 2 234. ½235. -9236. 1237. -8238. 3239. 1/6240. -1241. -3/7242. 13243. 10244. 24245. 0.86246. 11247. 3248. -7249. 2250. -4251. -6252. 2253. All Real Numbers254. No Solution255. 2256. All Real Numbers257. -24258. 2.9259. -7260. 7


261. ½262. -41263. All Real Numbers264. All Real Number265. 0266. No Solution267. 4268. -5269. 15270. 2271. -4 272. 21273. 7274. 6275. -11

276. 2277. 2278. Crickets: 187; Grasshoppers: 374279. A/l280. 3t-v281. (16c-2)/10282. 2A/b283. (3V)/(4r3)284. (P-2w)/2285. 5p-b286. (20x-8)/5287. V/2r2

288. 2A/(b1+b2)289. b290. a

Unit Review Answer Key

1. Are like terms2. Are unlike terms3. Are unlike terms4. Are unlike terms5. Are like terms6. Are like terms7. B8. D9. B10. D11. D12. A13. B14. B15. B16. C17. D18. C19. C20. C

21. B22. A23. B24. A25. C26. C27. B28. A29. C30. B31. D32. D33. A34. A35. A36. B37. C38. D39. C40. 4w + 1241. 2h – 442. 6m43. Answers will vary.44. 13 - 5x45. 240 miles

46. 547. x = 848. q = 949. e = 3

50. y = 13 47

51. b = −32

52. m = -4

53. x = 14

54. x = −174

55. v = 256. c = 0.557. a. 25 – 2g b. 23, 17, 13, 5, 1 tokens left58. a. number of people b. 8 c. 48 = 8p, p = number of people59. Answers will vary

60. m = b + 5, b = Bob’s age and m = Mary’s age

Bob Mary65 70


7075

7580

61. a. c = 0.45m + 40, c = total cost, m = number of minutes b. c = 0.35m + 70 c. Plan A62. No, only the problems with equations signs are equations, and there are only two equations.63. A. cost = $50.00 + $15.50x B. 29 members C. $95.2064. A. Rainbow Phone Service Company: p = $100.00 + $6.00x Cellular Phone Service Company: p = $80.00 + $10.00 x B. 5 data C. Rainbow Phone Service Company


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