Deck 5: Solving for the Unknown: a How-To Approach for Solving Equations

Question 1

6H + H - 20 = 44 - H; H = 8.

Answer 1

True

Question 2

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

Answer 2

True

Question 3

An equation represents a math expression of equality.

Answer 3

True

Question 4

Variables can only be numbers.

Question 5

B + 8 = 9; B = 17.

Question 6

2(V- 8) = 90; V = 53.

Question 7

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

Question 8

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

Question 9

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

Question 10

20(C - 9) means the 20 is multiplied only times the C to clear the parentheses.

Question 11

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

Question 12

4C stands for twice Cathy's age.

Question 13

4 + 3 = 9 is an equation of equality.

Question 14

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

Question 15

Variables and constants are terms of mathematical expressions.

Question 16

No number in front of a letter is really a 1.

Question 17

B - 11 = 40; B = 29.

Question 18

B/30 = 9; B = 270.

Question 19

A formula is not an equation.

Question 20

B - 6 represents Bob's age six years ago.

Question 21

Q + 92 = 128; Q equals:

A) -36
B) 36
C) 220
D) -220
E) None of these

Question 22

1/4B - 10 = 7; B = 67.

Question 23

B/8 = 90; B equals:

A) 8
B) 90
C) 72
D) 27
E) None of these

Question 24

A times C is represented by:

A) A:C
B) A + C
C) AC
D) A/C
E) None of these

Question 25

5(Z + 60) = 900; Z = 120.

Question 26

2,000(A - 5) = 110,000; A equals:

A) 6
B) 60
C) 600
D) 6,000
E) None of these

Question 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

Question 28

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

Question 29

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

Question 30

C + 100 = 55; C equals:

A) 45
B) 155
C) -155
D) -45
E) None of these

Question 31

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

Question 32

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

Question 33

What number decreased by 630 equals 1,510?

A) 880
B) 2,140
C) 4,120
D) 1,240
E) None of these

Question 34

N/8 + 6 = 58; N equals:

A) 512
B) 416
C) 521
D) 461
E) None of these

Question 35

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

Question 36

8G = 96; G equals:

A) 12
B) 21
C) -12
D) -21
E) None of these

Question 37

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

Question 38

+31 - (-16) equals:

A) 15
B) 47
C) -15
D) -47
E) None of these

Question 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

Question 40

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

Question 41

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

Question 42

Solve the following: 1,000(X - 2) = 75,000

A) 7
B) 77
C) 770
D) 7,700
E) None of these

Question 43

In Ryan Corporation, the first shift produced 5 1/2 times as many light bulbs as the second shift. If the total light bulbs produced were 16,250, how many light bulbs were produced on shift 1?

A) 2,500
B) 25,000
C) 1,375
D) 13,750
E) None of these

Question 44

In Johnson Corporation, the first shift produced 8 1/2 times as many light bulbs as the second shift. If the total light bulbs produced were 24,700, how many light bulbs were produced on shift 2?

A) 2,600
B) 22,100
C) 6,200
D) 22,010
E) None of these

Question 45

7G = 112; G equals:

A) -161
B) -112
C) 121
D) 16
E) None of these

Question 46

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

Question 47

P + 77 = 101; P equals:

A) 178
B) 22
C) 42
D) 24
E) None of these

Question 48

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

Question 49

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

Question 50

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 was the number of cartons of dolls? (Hint: Let T = cartons of dolls.)

A) 60
B) 70
C) 50
D) 30
E) None of these

Question 51

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

Question 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

Question 53

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

Question 54

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

Question 55

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

Question 56

Staples offer 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

Question 57

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 belts)

A) 17
B) 18
C) 16
D) 71
E) None of these

Question 58

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 shirts as polo shirts. How many casual shirts did Kohl's sell?

A) 80
B) 60
C) 40
D) 12
E) None of these

Question 59

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

Question 60

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

Question 61

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.

Question 62

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?
A. 150 T-shirts
B. 50 shorts

Question 63

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 = Pens)
A. 6 cartons of pens
B. 6 cartons of elastics

Question 64

7B - 70 = 140

Question 65

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.)

Question 66

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?

Question 67

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

Question 68

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?

Question 69

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?

Question 70

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

Question 71

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.)

Question 72

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

Question 73

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.)
A. 5 Cartons of pencils
B. 10 Cartons of erasers

Question 74

A furniture company produces 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?
A. Shift 1 produced 200
B. Shift 2 produced 800

Question 75

8 (A - 5) = 70

Question 76

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

Question 77

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?

Question 78

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?
A. 64 Boxes of diskettes
B. 8 Boxes of paper

Question 79

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