Slater Solving For The Unknown Exam Questions Chapter 4

Chapter 04

Solving for the Unknown

True/False Questions
 

1. An equation represents a math expression of equality. 
True    False

2. 4 + 3 = 9 is an equation of equality. 
True    False

3. Variables can only be numbers. 
True    False

4. No number in front of a letter is really a 1. 
True    False

5. AB or A(B) means A divided by B. 
True    False

6. C/D means C divided by D. 
True    False

7. 4C stands for twice Cathy's age. 
True    False

8. B – 6 represents Bob's age six years ago. 
True    False

9. Whatever you do to one side of an equation, you must do to the other. 
True    False

10. A formula is not an equation. 
True    False

11. Variables and constants are terms of mathematical expressions. 
True    False

12. B + 8 = 9; B = 17. 
True    False

13. B – 11 = 40; B = 29. 
True    False

14. When an equation uses addition, the variable can be solved by the opposite process: subtraction. 
True    False

15. B/30 = 9; B = 270. 
True    False

16. B/5 + 3 = 15; B = 16. 
True    False

17. 20(C – 9) means the 20 is multiplied only times the C to clear the parentheses. 
True    False

18. 2(V – 8) = 90; V = 53. 
True    False

19. 6H + H – 20 = 44 – H; H = 8. 
True    False

20. In word problems, the word "of" indicates an equal sign. 
True    False

21. More than one unknown in a word problem can be represented in terms of the same variable assigned to first unknown. 
True    False

22. There is only one set way to solve all word problems. 
True    False

23. If there are two unknowns, the variable is always assigned to the larger value. 
True    False

24. 1/4B – 10 = 7; B = 67. 
True    False

25. 5(Z + 60) = 900; Z = 120. 
True    False

Multiple Choice Questions
 

26. A letter or a symbol that represents one or more numbers is a: 
A. Variable
B. Equation
C. Known
D. Constant
E. None of these

27. An equation is: 
A. A math expression of inequality
B. A math expression of constants
C. A math unknown
D. A math expression of equality
E. None of these

28. A times C is represented by: 
A. A:C
B. A + C
C. AC
D. A/C
E. None of these

29. Jerry's age 10 years ago can be expressed as: 
A. A – 10
B. A + 10
C. 2A – 10
D. 2A + 10
E. None of these

30. +31 – (–16) equals: 
A. 15
B. 47
C. –15
D. –47
E. None of these

31. C + 100 = 55; C equals: 
A. 45
B. 155
C. –155
D. –45
E. None of these

32. Q + 92 = 128; Q equals: 
A. –36
B. 36
C. 220
D. –220
E. None of these

33. 8G = 96; G equals: 
A. 12
B. 21
C. –12
D. –21
E. None of these

34. B/8 = 90; B equals: 
A. 8
B. 90
C. 72
D. 27
E. None of these

35. N/8 + 6 = 58; N equals: 
A. 512
B. 416
C. 521
D. 461
E. None of these

36. 2,000(A – 5) = 110,000; A equals: 
A. 6
B. 60
C. 600
D. 6,000
E. None of these

37. What number decreased by 630 equals 1,510? 
A. 880
B. 2,140
C. 4,120
D. 1,240
E. None of these

38. What number increased by 3,080 equals 5,082? 
A. 2,020
B. 18,126
C. 8,162
D. 2,002
E. None of these

39. One-ninth of all sales at a local Subway are for cash. If cash sales for the week were $690, what were Subway’s total sales? 
A. $2,610
B. $22,600
C. $6,210
D. $2,611
E. None of these

40. One-eleventh of all sales at Joe's Diner are for cash. If cash sales for the week were $380, what were Joe's total sales? 
A. $41,800
B. $4,180
C. $4,108
D. $41,808
E. None of these

41. Jane sells 8 times as many Volvos as Melissa. If the difference in their sales is 35, how many cars did Jane sell? 
A. 35
B. 5
C. 45
D. 40
E. None of these

42. Lane is 10 times Mel's age. If the difference in their age is 27, how old is Mel? 
A. 3
B. 4
C. 30
D. 26
E. None of these

43. Rick and Ranger sell Toyotas for Tom's Auto. Over the past year they sold 360 cars. Assuming Rick sells 5 times as many as Ranger, how many Toyotas did Ranger sell? 
A. 180
B. 240
C. 300
D. 60
E. None of these

44. Mike and Bill sell cars for Jangle's Auto. Over the past year they sold 640 cars. Assuming Mike sells 3 times as many as Bill, how many cars did Mike sell? 
A. 480
B. 160
C. 180
D. 500
E. None of these

45. Staples sells CDs ($2.00) and boxes of computer paper ($3). If total sales were $1,560 and customers bought 5 times as many CDs as boxes of computer paper, how many CDs were sold? 
A. 120
B. 480
C. 600
D. 1,200
E. None of these

46. A local Walmart sells sweatpants ($7) and jackets ($14). If total sales were $6,160 and customers bought 8 times as many sweatpants as jackets, what would be the number of jackets sold? 
A. 880
B. 8
C. 88
D. 8,880
E. None of these

47. At Shaw's Market, apples cost $10 per case and bananas cost $6 per case. If an order comes in for a total of 300 cases for $2,000, what was the specific number of cases of apples? (Hint: Let A = cases of apples.) 
A. 5
B. 15
C. 50
D. 200
E. None of these

48. Coffee costs $12 per case, and tea costs $8 per case. If an order comes in for a total of 250 cases for $2,600, what was the specific number of cases of tea? (Hint: Let C = cases of coffee.) 
A. 150
B. 100
C. 1,800
D. 800
E. None of these

49. Dolls cost $140 per carton, and trucks cost $430 per carton. If an order comes in for a total of 100 cartons for $28,500, what is the number of cartons of dolls? (Hint: Let T = cartons of trucks.) 
A. 60
B. 70
C. 50
D. 30
E. None of these

50. Belts cost $160 per carton, and shoes cost $465 per carton. If an order comes in for a total of 88 cartons for $19,265, what is the number of cartons of belts? (Hint: Let S = cartons of shoes.) 
A. 17
B. 18
C. 16
D. 71
E. None of these

51. Marvin Co. sells pens ($6) and flashlights ($10). If total sales were $624 and customers bought 7 times as many pens as flashlights, what would be the number of pens sold? 
A. 12
B. 62
C. 84
D. 48
E. None of these

52. Jill Co. sells thermometers ($2) and hot water bottles ($6). If total sales were $312 and customers bought 10 times as many thermometers as hot water bottles, what would be the number of hot water bottles sold? 
A. 120
B. 119
C. 12
D. 11
E. None of these

53. In Ryan Corporation, the first shift produced 5 1/2 times as many lightbulbs as the second shift. If the total lightbulbs produced was 16,250, how many lightbulbs were produced on shift 1? 
A. 2,500
B. 25,000
C. 1,375
D. 13,750
E. None of these

54. In Johnson Corporation, the first shift produced 8 1/2 times as many lightbulbs as the second shift. If the total lightbulbs produced was 24,700, how many lightbulbs were produced on shift 2? 
A. 2,600
B. 22,100
C. 6,200
D. 22,010
E. None of these

55. Joe Berry and Jane Rose received a total of $180,000 from a deceased relative's estate. They decided to put away $80,000 in a trust for their child and divide the remainder into 3/4 for Jane and 1/4 for Joe. How much will Jane receive? 
A. $25,000
B. $75,000
C. $20,000
D. $80,000
E. None of these

56. Al Resse and Marci Rey received a total of $210,000 from a deceased relative's estate. They decided to put away $50,000 in a trust for their child and divide the remainder into 1/4 for Marci and 3/4 for Al. How much will Al receive? 
A. $40,000
B. $120,000
C. $32,000
D. $10,000
E. None of these

57.  7G = 112; G equals:

A. –161

B. –112

C. 121

D. 16

E. None of these

58. P + 77 = 101; P equals:

A. 178

B. 22

C. 42

D. 24

E. None of these

59. Scholastic Books sells 4 times as many textbooks as Keller Publishing; together they sold 7,775 textbooks. How many did Scholastic sell?

A. 9,330

B. 1,555

C. 6,220

D. 6,022

E. None of these

60. Solve the following:

1,000(X – 2) = 75,000:

A. 7

B. 77

C. 770

D. 7,700

E. None of these

61. Kohl’s sells casual shirts for $9 and polo shirts for $18.00. Total sales were $1,080, and customers bought 4 times as many casual as polo shirts. How many casual shirts did Kohl’s sell?

A. 20

B. 60

C. 40

D. 12

E. None of these

Short Answer Questions
 

62. 1. Equations
2. Formula
3. Constant
4. Unknowns
5. Variables
6. G
7. 2
8. Parenthesis
9. Blueprints
A. I = P × R × T
B. 1 G
C. Attempting to solve for
D. Negative
E. A match statement of equality
F. Teaching aid
G. + 2
H. + 3
I. Multiplication or grouping
J. A constant
K. Letters or symbols 

63. Solve for the unknown, showing all work. (If necessary, round to the nearest hundredth.)
A + 80 = 165 

64. Solve for the unknown, showing all work. (If necessary, round to the nearest hundredth.)
1,105 = B + 82 

65. Solve for the unknown, showing all work. (If necessary, round to the nearest hundredth.)
Q/40 = 20 

66. Solve for the unknown, showing all work. (If necessary, round to the nearest hundredth.)
6B – 80 = 160 

67. Solve for the unknown, showing all work. (If necessary, round to the nearest hundredth.)
7 (A – 4) = 21 

68. Solve for the unknown, showing all work. (If necessary, round to the nearest hundredth.)
8A – 40 = 4A + 60 

69. Over the past month, 900 trucks were sold. Abe sold 4 times as many as Joe. How many did each sell?
A. ____________ Abe
B. ____________ Joe 

70. A furniture company produced 5 times as many beds on shift 2 as it did on shift 1. If a total of 240 beds were produced, how many were produced on each shift?
A. ____________ Shift 1
B. ____________ Shift 2 

71. 1/9 of all sales were for cash. If cash sales were $59,000, what were the total sales? 

72. One day Marika Company produced 6 times as many wood stoves as Barry Company. If the difference in their production is 15, how many stoves did Barry produce that day? 

73. Runyon Company sells T-shirts ($5) and shorts ($6). If total sales were $1,040 and people bought 4 times as many T-shirts as shorts, what would be the number of T-shirts and shorts sold?
A. ___________ T-shirts
B. ___________ Shorts 

74. Erasers cost $6 per carton, and pencils cost $7 per carton. If an order comes in for a total of 16 cartons for $100, what was the number of cartons of each bought? (Hint: Let pencils = p.)
A. ______________ Pencils
B. ______________ Erasers 

75. American Airlines reduced its round trip fare from Boston to New York by $45. The sale price was $139. What was the original price? 

76. Ryan Small budgets 1/8 of his weekly salary for food. Ryan's food bill is $80. What is his weekly salary? 

77. If Sears Roebuck sells six times as many batteries as Firestone and their difference in sales is 250,000 batteries, how many batteries did each sell? 

78. Jim Murray and Al Sming sold a total of 600 camcorders. Jim sold 5 times as many camcorders as Al. How many did each sell? 

79. Brian Smith sells sets of movie posters ($12) and baseball cards ($8) at a local flea market. Last Sunday, Brian's total sales were $840. People bought 4 times as many movie posters as baseball cards. How many of each did Brian sell? Check your answer. 

80. Peter Mabet sold a total of 400 oatmeal ($1.50) and wheat ($2) breads during the Labor Day weekend. How many of each did Peter sell if total sales were $700? Check your answer. (Let W = wheat.) 

81. A + 20 = 55 

82. 1,080 = B + 30 

83. 7B – 70 = 140 

84. 8 (A – 5) = 70 

85. 10A – 20 = 4A + 80 (answer to closest hundredth). 

86. B + 40 = 90 

87. 2,015 = Q + 90 

88. 5A – 10 = 90 

89. 10 (C – 7) = 30 

90. 20A – 40 = 8A + 160 (answer to nearest hundredth). 

91. Over the past month, 700 trucks were sold. Abe sold 6 times as many as Joe. How many did each sell? 

92. A furniture company produced 4 times as many beds on shift 2 as on shift 1. If a total of 1,000 beds were produced, how many were produced on each shift? 

93. 1/7 of all sales were for cash. If cash sales were $28,000, what were the total sales? 

94. Marika is 8 times Barry's age. If the difference in their age is 7 years, how old is Marika? 

95. Runyon Co. sells T-shirts ($4) and shorts ($5). If total sales were $850 and people bought 3 times as many T-shirts as shorts, what would be the number of T-shirts and shorts sold? 

96. Erasers cost $5 per carton, and pencils cost $7 per carton. If an order comes in for a total of 15 cartons for $85, what number of cartons of each was bought? (Hint: Let cartons of pencils = P.) 

97. The Rand Co. produces 11 times as many rings on shift 1 as on shift 2. If a total of 12,000 rings were produced, how many were produced on each shift? 

98. Over the past month, 900 telephones were serviced. If Jill services 8 times as many phones as Rose, how many did each service? 

99. 1/5 of all sales were for cash. If cash sales were $4,000, what were total sales? 

100. Moe is 6 times Al's age. If the difference in their ages is 20, how old is Moe? 

101. The Computer Store sells diskettes ($2) and boxes of computer paper ($7). If total sales were $184 and customers bought 8 times as many diskettes as boxes of computer paper, what would be the number of each sold? 

102. Pens cost $6 per carton, and elastics cost $4 per carton. If an order comes in for a total of 12 cartons for $60, what was the specific number of cartons of pens as well as elastics? (Hint: Let P = cartons of pens.) 

103. Andy Foll is 6 times as old as Mel Kaas. Andy is 15 years older than Mel. What is Mel's age? 

104. Art Neuner and Paul Kosponato sell trucks for Blue Auto. Over the past year, they sold 240 trucks. Assuming Paul sells 7 times as many as Art, how many trucks did each sell? 

105. 1/8 of all wood stoves are sold for cash. If cash sales were $2,200 for the week, what was the total of all sales? (Let S = sales.) 

106. Wrenches cost $50 per carton, and hammers cost $150 per carton. If an order comes in for a total of 60 cartons for $5,000, what was the number of cartons of wrenches as well as hammers? (Hint: Let cartons of hammers = H.) 

107. The cost of oil is 6 times the cost of wood. The total bill for oil and wood is $700. What was the expense for each? 

108. Jane weighs 12 pounds less than Shelley. Assuming Jane weighs 120 pounds, find Shelley's weight. 

109. Mick and Mack went to a supermarket and bought boxes of soap detergent. Mack could buy only four boxes, which was 1/5 as much as Mick. How many boxes did Mick buy? 

110. Jarvis Co. sells thermometers ($3) and hot water bottles ($7). If total sales were $760 and customers bought 4 times as many thermometers as hot water bottles, what would be the number of each sold? (Let B = number of hot water bottles.) 

111. At Miduale Electronics, the first shift produced 6 times as many items as the second shift. If total production was 4,900, what was the output for each shift? 

112. Melons cost $20 per crate, and apples cost $8 per crate. An order comes in for a total of 48 crates for $420. What was the number of crates of melons and apples? (Let crates of melons = M.) 

113. JCP sold a pair of pants that was reduced by $12.00. The selling price was $48.00. What was the original price?

114. Momentum Electronics produces 4 times as many E-readers on shift 1 as it does on shift 2. If a total of 85 E-readers were produced, how many were made on shift 1?

115. Cecil budgets 1/6 of his weekly salary for comic books. Cecil’s weekly bill is $30.00. What is his weekly salary?

116. Riley and Ayu sold a total of 1,080 iPads. Riley sold 7 times as many as Ayu. How many did each sell?

117. Mark Greffet sells air fresheners for automobiles for $6.00 and cans of powdered air freshener for $4.00. Total sales were $196. Customers bought 4 times as many air fresheners as powdered air cans. How many of each were sold? What was the total dollar value sold for each?