Deck 4: Formulas and Problem Solving

Question 1

The cross products of a proportion are equal to each other.

Answer 1

True

Question 2

Solve the equation. $\frac { - 8 } { x + 7 } = \frac { - 9 } { x - 8 }$

A) x = -125
B) x = -122
C) x = -127
D) x = -136
E) x = -128

Answer 2

x = -127

Question 3

Solve the equation. $\frac { n + 7 } { n } = \frac { 8 } { 7 }$

A) n = 49
B) n = 54
C) n = 48
D) n = 51

Answer 3

n = 49

Question 4

What is 6% of 22?

A) 1.32
B) 3.42
C) 1.29
D) 6.43

Question 5

Solve the equation. $\frac { x + 4 } { 5 } - \frac { x + 3 } { 6 } = 6$

A) x = 180
B) x = 171
C) x = 176
D) x = 170

Question 6

Change the fraction $\frac { 7 } { 25 }$ to a percent.

A) 30%
B) 27%
C) 28%
D) 33%

Question 7

The equation $\frac { 3 } { 3 x + 1 } + 1 = \frac { 4 } { 4 x - 3 }$ is a proportion.

Question 8

18% of what number is 8.46?

A) 47
B) 41
C) 49
D) 52

Question 9

Jesse used 5 gallons of gasoline to drive 75 miles. How much gasoline will he need to travel 240 miles?

A) 18 gallons
B) 21 gallons
C) 16 gallons
D) 12 gallons

Question 10

Solve the equation. $\frac { n } { 104 - n } = \frac { 11 } { 2 }$

A) n = 93
B) n = 90
C) n = 88
D) n = 87

Question 11

A percent is never greater than 100.

Question 12

A statement of inequality between two ratios is called a proportion.

Question 13

43.56 is what percent of 66?

A) 73%
B) 66%
C) 69%
D) 57%
E) 62%

Question 14

Solve the equation. $\frac { - 3 } { x + 8 } = \frac { - 4 } { x - 8 }$

A) x = -51
B) x = -57
C) x = -54
D) x = -56
E) x = -65

Question 15

Solve the equation. $\frac { x } { 20 } = \frac { 3 } { 4 }$

A) x = 14
B) x = 15
C) x = 20
D) x = 17

Question 16

If the ratio of the width of a rectangle to its length is $\frac { 4 } { 5 }$ and the length is 40 centimeters, find the width.

A) 34 cm
B) 28 cm
C) 32 cm
D) 37 cm

Question 17

On a certain map, 1 inch represents 15 miles. If two cities are 5 inches apart on the map, find the number of miles between the cities.

A) 77 mi
B) 65 mi
C) 75 mi
D) 80 mi

Question 18

Solve the equation. $\frac { x - 9 } { 3 } = \frac { x + 6 } { 4 }$

A) x = 54
B) x = 59
C) x = 53
D) x = 56

Question 19

Solve the equation. $\frac { x - 4 } { 16 } - 7 = \frac { 1 } { 8 }$

A) x = 117
B) x = 120
C) x = 123
D) x = 118

Question 20

Solve the equation. $\frac { h } { 5 } - \frac { h } { 6 } = 8$

A) h = 239
B) h = 245
C) h = 242
D) h = 240

Question 21

If 20 pounds of fertilizer will cover 1,490 square feet of lawn, how many pounds are needed for 2,980 square feet?

A) 42 pounds
B) 40 pounds
C) 30 pounds
D) 45 pounds

Question 22

11% of what number is 5.39?

Question 23

Solve the equation.

Question 24

A saltwater solution is made by dissolving 5 pounds of salt in 14 gallons of water. At this rate, how many pounds of salt are needed for 28 gallons of water.

A) 140 pounds
B) 10 pounds
C) 12 pounds
D) 7 pounds

Question 25

Solve the equation.

Question 26

Solve the equation.

Question 27

20% of what number is 7.4?

Question 28

Solve the equation.

Question 29

Solve the equation.

Question 30

A board 55 feet long is cut into two pieces whose lengths are in the ratio of 2 to 9. Find the lengths of the two pieces.

A) 10 feet, 45 feet
B) 15 feet, 40 feet
C) 9 feet, 46 feet
D) 7 feet, 48 feet

Question 31

Solve the equation.

Question 32

Solve the equation.

Question 33

Solve the equation.

Question 34

Change the fraction to a percent.

Question 35

Solve the equation.

Question 36

An inheritance of $234,000 is to be divided between a child and the local cancer fund in the ratio of 1 to 5. How much money will the child receive?

A) $38,750
B) $38,500
C) $40,500
D) $39,000
E) $40,000

Question 37

What is 7% of 22?

Question 38

An donation of $440,000 is to be divided between the YMCA and the local food bank in the ratio of 8 to 3. How much money will the YMCA receive?

A) $319,750
B) $319,500
C) $321,500
D) $320,000
E) $321,000

Question 39

The ratio of male students to female students at a certain university is 2 to 9. If there is a total of 7,271 students, find the number of male students and the number of female students.

A) male 1,322, female 5,949
B) male 5,969, female 1,302
C) male 1,332, female 5,939
D) male 1,325, female 5,946
E) male 5,949, female 1,322

Question 40

A saltwater solution is made by dissolving 7 pounds of salt in 10 gallons of water. At this rate, how many pounds of salt are needed for 40 gallons of water?

A) 28 pounds
B) 25 pounds
C) 280 pounds
D) 30 pounds
E) none of these

Question 41

Solve the following equation. Your calculator might be of some help. 0.4 x + 9.6(589 $-$ x ) = 3,141

A) x = 956
B) x = 925
C) x = 979
D) x = 968
E) none of these

Question 42

Jesse used 10 gallons of gasoline to drive 140 miles. How much gasoline will he need to travel 168 miles? __________ gallons

Question 43

Selling price is the cost minus the profit.

Question 44

A saltwater solution is made by dissolving 2 pounds of salt in 14 gallons of water. At this rate, how many pounds of salt are needed for 70 gallons of water. __________ pounds

Question 45

A board 26 feet long is cut into two pieces whose lengths are in the ratio of 4 to 9. Find the lengths of the two pieces. Please enter your answer as two numbers without the units, listed from least to greatest, separated by a comma.

Question 46

What is 4% of 38? Give the answer to two decimal places, if necessary.

Question 47

Profit is always a percent of the selling price.

Question 48

If the ratio of the width of a rectangle to its length is and the length is 72 centimeters, find the width. __________ centimeters

Question 49

If the store advertises a 30% off sale, the price of an item is $( 0.70 )$ (original price of item).

Question 50

If 21 pounds of fertilizer will cover 1,400 square feet of lawn, how many pounds are needed for 2,800 square feet? __________ pounds

Question 51

Solve the equation. 0.34 x + 0.37( x + 382) = 323.81

A) x = 276
B) x = 267
C) x = 224
D) x = 257
E) none of these

Question 52

A saltwater solution is made by dissolving 5 pounds of salt in 8 gallons of water. At this rate, how many pounds of salt are needed for 40 gallons of water. __________ pounds

Question 53

An inheritance of $180,000 is to be divided between a child and the local cancer fund in the ratio of 2 to 3. How much money will the child receive? $__________

Question 54

On a certain map, 1 inch represents 13 miles. If two cities are 8 inches apart on the map, find the number of miles between the cities. __________ miles

Question 55

Solve the following equation and express the solution in decimal form. Your calculator might be of some help. 1.9 x + 9.1 = 11.513

A) x = 1.27
B) x = 1.37
C) x = 1.77
D) x = 1.25
E) none of these

Question 56

Solve the equation. x $-$ 0.15 = 0.62

A) x = 0.77
B) x = 1.24
C) x = 0.47
D) x = $-$ 0.47
E) none of these

Question 57

Solve the equation. 0.45 t = 0.36

A) t = 0.8
B) t = 1.3
C) t = 1.7
D) t = 0.6
E) none of these

Question 58

62.48 is what percent of 71?

Question 59

The discount is the percent off times the original selling price.

Question 60

Solve the equation. s = 9.8 + 0.8 s

A) s = 58
B) s = 46
C) s = 49
D) s = 53
E) none of these

Question 61

Find the cost of a $3,000 refrigerator that is on sale for 40% off.

A) $1,800
B) $7,500
C) $2,960
D) $4,200
E) none of these

Question 62

If a sofa costs a retailer $420, at what price should it be sold to gain a profit of 65% of the selling price?

A) $721.00
B) $678.00
C) $695.00
D) $693.00
E) none of these

Question 63

Tom bought an electric drill at a 5% discount sale for $25.65. What was the original price of the electric drill?

A) $27
B) $46
C) $41
D) $24
E) none of these

Question 64

Use the formula $i = P r t$ to reach a solution for the following problem. One month a credit card company charged $29.25 in interest on a balance of $3,900. What annual interest rate is the credit card company charging?

A) 11%
B) 9%
C) 8%
D) 9.5%
E) none of these

Question 65

Use the formula $i = P r t$ to reach a solution for the following problem. How long (in years) will $7,560 need to be invested at a 7% annual interest rate to earn $2,646.00?

A) t = 4
B) t = 5
C) t = 7
D) t = 10
E) none of these

Question 66

Use the formula $i = P r t$ to reach a solution for the following problem. How much principal, invested at 18% annual interest for 6 years, is needed to earn $4,039.20?

A) P = $3,740
B) P = $3,810
C) P = $3,730
D) P = $3,700
E) none of these

Question 67

Solve the following equation. Your calculator might be of some help. 2.8( x + 4.5) = 15.96

A) x = 2.4
B) x = 1.2
C) x = 0.9
D) x = 1.8
E) none of these

Question 68

Find the cost of a $4,700 wide-screen television that is on sale for 25% off.

A) $3,532
B) $3,539
C) $3,546
D) $3,525
E) $3,553

Question 69

Use the formula $i = P r t$ to reach a solution for the following problem. How much interest will be charged on a student loan if $8,820 is borrowed for 4 months at a 18% annual interest rate?

A) $530.40
B) $534.20
C) $529.20
D) $525.70
E) none of these

Question 70

A retailer has some candle sets that cost her $24. If she sells them for $30.00, find her rate of profit based on the cost.

A) 20%
B) 24%
C) 27%
D) 25%
E) none of these

Question 71

A retailer has some earrings that cost him $6 each. He wants to sell them at a profit of 75% of the cost. What should be the selling price of the earrings?

A) $18.50
B) $11.50
C) $8.50
D) $10.50
E) none of these

Question 72

Use the formula $i = P r t$ to reach a solution for the following problem. For how many years must $5,590 be invested at a 8% annual interest rate to earn $2,683.20?

A) t = 11
B) t = 5
C) t = 6
D) t = 8
E) none of these

Question 73

A retailer has some toe rings that cost him $5 each. He wants to sell them at a profit of 40% of the cost. What should be the selling price of the toe rings?

A) $10.00
B) $7.00
C) $2.00
D) $9.00
E) none of these

Question 74

Jewelry has a very high markup rate. If a ring costs a jeweler $680, at what price should it be sold to gain a profit of 45% of the selling price?

A) $993.00
B) $973.00
C) $986.00
D) $1,017.00
E) none of these

Question 75

Pierre bought a coat for $213.20 that was listed for $260. What rate of discount did he receive?

A) 12%
B) 28%
C) 21%
D) 18%
E) none of these

Question 76

Solve the equation. x 0.47 = 0.76 Please enter your answer as a decimal.

Question 77

Use the formula $i = P r t$ to reach a solution for the following problem. How much is a month s interest on a mortgage balance of $2,640 at an 7% annual interest rate?

A) $185.80
B) $15.40
C) $184.80
D) $30.80
E) none of these

Question 78

Dale bought a boat at a 20% discount sale for $50.40. What was the original price of the boat?

A) $82
B) $63
C) $81
D) $55
E) none of these

Question 79

A retailer has some skirts that cost her $25. If she sells them for $32.75, find her rate of profit based on the cost.

A) 26%
B) 33%
C) 31%
D) 30%
E) none of these

Question 80

Use the formula $i = P r t$ to reach a solution for the following problem. Find the annual interest rate if $2,616.00 in interest is earned when $2,180 is invested for 8 years.

A) 14%
B) 20%
C) 16%
D) 15%
E) none of these