Deck 4: Ratios, Rates, and Proportional Reasoning

Question 1

Write each ratio in two other ways. 6 to 5

A) $\frac { 7 } { 5 }$ ; $7 : 5$
B) $\frac { 5 } { 6 }$ ; $5 : 6$
C) $\frac { 6 } { 5 }$ ; $6 : 5$
D) $\frac { 5 } { 5 }$ ; $5 : 5$
E) $\frac { 6 } { 4 }$ ; $6 : 4$

Answer 1

$\frac { 6 } { 5 }$ ; $6 : 5$

Question 2

Write a ratio from the sentence and simplify it, possible. Frantisek adds 2 cans of milk to a can of soup.

A) $3$ to 1
B) 1 to $2$
C) $2$ to 1
D) $1$ to 1
E) 1 to $3$

Answer 2

$2$ to 1

Question 3

Simplify the ladder ratio below. State whether it is a safe ladder ratio. If the ladder ratio is greater than 4:1 it is likely to tip. If the ladder ratio is less than 4:1, it is likely to slip. 12 feet to 2.4 feet

A) 1 to 2; tip
B) 1 to 2; slip
C) 5 to 1; tip
D) 5 to 1; slip
E) 2 to 1; slip

Answer 3

5 to 1; tip

Question 4

Change the units to like units with a unit analysis multiplication, and simplify the ratio. Useful facts:
1 yard = 3 feet
1 mile = 5,280 feet
1 yard = 36 inches
2 feet to 3 inches

A) 18 to 1
B) 2 to 3
C) 12 to 1
D) 1 to 18
E) 8 to 1

Question 5

Solve. $\frac { 18 } { 24 } = \frac { n } { 8 }$

A) 18
B) 1.5
C) 54
D) 6
E) 3

Question 6

Solve. Round to the nearest hundredth. $\frac { 3 } { 4 } = \frac { 11 } { n }$

A) 14.67
B) 1.09
C) 44.00
D) 0.11
E) 12.00

Question 7

Jasmin budgets the following each month: rent, $400; utilities, $140; food, $320; clothes, $110; car payment and insurance, $470; gasoline, $60; savings, $20; other $80. What percent of her total monthly budget does she spend on car payment and insurance?

A) 36 $\frac { 1 } { 4 }$ %
B) 25%
C) 29 $\frac { 3 } { 8 }$ %
D) 6 $\frac { 4 } { 5 }$ %
E) 18%

Question 8

Write the staircase slope in fraction notation and simplify it to lowest terms. Both measures are in inches, so units may be disregarded. 6.25 to 11.75

A) $\frac { 25 } { 47 }$
B) $\frac { 27 } { 47 }$
C) $\frac { 23 } { 47 }$
D) $\frac { 6.1 } { 11.3 }$
E) $\frac { 61 } { 113 }$

Question 9

Solve. $\frac { n } { 6 } = \frac { 5 } { 15 }$

A) 3
B) 5
C) 2
D) -5
E) 6

Question 10

Solve. Round to the nearest hundredth. $\frac { 1 } { 4 } = \frac { n } { 14 }$

A) 0.25
B) 14.00
C) 3.50
D) 0.29
E) 0.07

Question 11

Notation can make problems look harder than they are. Water with formula H₂O has 2 atoms of hydrogen for each atom of oxygen. A molecule of nicotine, C₁₀H₁₄N₂, has 10 atoms of carbon, 14 atoms of hydrogen, and 2 atoms of nitrogen. What is the ratio of atoms in the following chemical formula? (Ca is calcium) CaCO₃

A) 1 calcium to 1 carbon to 1 oxygen
B) 3 calcium to 1 carbon to 1 oxygen
C) 1 calcium to 3 carbon to 1 oxygen
D) 1 calcium to 1 carbon to 3 oxygen
E) 3 calcium to 3 carbon to 3 oxygen

Question 12

Write a ratio of fertilizer to water and simplify it, if possible. Useful facts:
16 tablespoons = 1 cup
16 cups = 1 gallon
Sylvia adds 8 tablespoons of plant fertilizer to a gallon of water.

A) 1 to 4
B) 1 to 32
C) 1 to 64
D) 1 to 128
E) 1 to 8

Question 13

Change 100 miles per hour to feet per second. Start with a fraction showing miles per hour, and then set up the unit analysis product of fractions. Useful facts:
5280 feet = 1 miles
60 seconds = 1 minute
60 minutes = 1 hour

A) 146 $\frac { 2 } { 3 }$ feet per second
B) 146 $\frac { 1 } { 3 }$ feet per second
C) 161 $\frac { 2 } { 3 }$ feet per second
D) 68 $\frac { 2 } { 11 }$ feet per second
E) 144 $\frac { 1 } { 3 }$ feet per second

Question 14

Write a ratio of water to fruit drink and simplify it, if possible. Sergei adds 2 cans of water to each can of frozen fruit drink.

A) 2 to 1
B) 2 to 3
C) 1 to 2
D) 3 to 2
E) 3 to 1

Question 15

Change the units to like units with a unit analysis multiplication, and simplify the ratio. Useful facts:
1,000 milliliters = 1 liter
1,000 meters = 1 kilometer
5,280 feet = 1 mile
750 meters to 2 kilometers

A) $\frac { 5 } { 8 }$
B) $\frac { 8 } { 3 }$
C) $\frac { 3 } { 8 }$
D) $\frac { 4 } { 3 }$
E) $\frac { 3 } { 4 }$

Question 16

Write the ratio in two other ways. 9 : 8

A) $\frac { 9 } { 8 } , 9 \text { to } 8$
B) $\frac { 9 } { 8 } , 8 \text { to } 9$
C) $\frac { 8 } { 9 } , 9 \text { to } 8$
D) $\frac { 8 } { 9 } , 8 \text { to } 9$
E) $\frac { 17 } { 8 } , 17 \text { to } 8$

Question 17

Write each ratio in two other ways. $\frac { 5 } { 10 }$

A) $6 : 10$ , $6$ to $10$
B) $5 : 11$ , $5$ to $11$
C) $5 : 10$ , $5$ to $10$
D) $4 : 10$ , $4$ to $10$
E) $5 : 9$ , $5$ to $9$

Question 18

Solve. $\frac { 6 } { n } = \frac { 10 } { 15 }$

A) 90
B) 1.5
C) 15
D) 9
E) 60

Question 19

Find the slope ratio for the equation. $y = 1.75 x + 5.75$

A) $\frac { 7 } { 23 }$
B) $\frac { 23 } { 7 }$
C) $\frac { 3 } { 2 }$
D) $\frac { 7 } { 4 }$
E) $\frac { 9 } { 4 }$

Question 20

Solve. $\frac { 2 } { 6 } = \frac { 4 } { n }$

A) 1.5
B) 12
C) 3
D) 6
E) 24

Question 21

A loading ramp with a ratio of $\frac { 1 } { 6 }$

A) $15.67$ %
B) $17.67$ %
C) $16.67$ %
D) $18.67$ %
E) $14.67$ %

Question 22

Alex just received a 25% salary increase. If her new salary is $3000, what was her old salary?

A) $3,750
B) $2,400
C) $2,250
D) $2,370
E) $2,440

Question 23

Write the percent problems as equations or proportions and solve. Round to the nearest tenth or tenth of percent. 56 is what percent of 85 ?

A) $64.9$ %
B) $66.9$ %
C) $67.9$ %
D) $63.9$ %
E) $65.9$ %

Question 24

The shadow of a pole at 2 p.m. is 4 feet. The shadow of nearby 10-inch-tall squirrel is 4 inches. How tall is the pole?

A) $11$ ft
B) $9$ ft
C) $12$ ft
D) $10$ ft
E) $8$ ft

Question 25

Use ratios to find out if the triangles are similar.

A) Similar
B) Not similar

Question 26

An access ramp needs to rise 24 inches. If the ramp is to have a slope ratio of 1:8, what horizontal distance is needed to build the ramp? Give the answer in feet.

A) 16 feet
B) 14 feet
C) 3 feet
D) 11 feet
E) 192 feet

Question 27

Write the percent problem as a proportion or equation and solve. Round to the nearest tenth or tenth of a percent. 111 is what percent of 60?

A) 54.1%
B) 195%
C) 185%
D) 200%
E) 66.6%

Question 28

Write the percent problem as a proportion or equation and solve. Round to the nearest tenth or tenth of a percent. 85% of what number is 68?

A) 80
B) 85
C) 65
D) 57.8
E) 125

Question 29

Tell what percent grade is described. A wheelchair ramp with a ratio of 1 to 17.

A) $5 \frac { 17 } { 15 }$ %
B) $5 \frac { 3 } { 15 }$ %
C) $5 \frac { 15 } { 6 }$ %
D) $5 \frac { 15 } { 17 }$ %
E) $5 \frac { 15 } { 1 }$ %

Question 30

The oil in a lawn mower needs to be changed every 28 hours. If the mower travels 100 feet in 30 seconds and shuts off when stopped, how many miles will it travel between oil changes?

A) 63.4 mi
B) 63.6 mi
C) 64.0 mi
D) 64,2 mi
E) 64.4 mi

Question 31

Find the unknown side, n, in the following pair of similar figures. Round your answer to one decimal place.

A) 32.5
B) 31.5
C) 26.5
D) 33.5
E) 34.5

Question 32

At 3:00 p.m., 29-foot tree casts 36-foot shadow.A person 4 feet tall will cast how long a shadow? Round the nearest tenth.

A) $7.0$ ft
B) $6.0$ ft
C) $5.0$ ft
D) $8.0$ ft
E) $2.0$ ft

Question 33

Find the ending value for the given percent change. A $120 stock gains 20% of its value.

A) $ 144
B) $ 140
C) $ 154
D) $ 24
E) $ 124

Question 34

Write the percent problems as equations or proportions and solve. Round to the nearest tenth or tenth of percent. 70% of what number is 39?

A) $56.7$
B) $54.7$
C) $57.7$
D) $55.7$
E) $53.7$

Question 35

Solve. Round to the nearest hundredth. $$\frac { n } { 17 } = \frac { 23 } { 9 }$$

A) 2.56
B) 12.18
C) 1.35
D) 43.44
E) 391.00

Question 36

Solve the unit problem using the conversion information. Use either a proportion or unit analysis. Round to the nearest hundredth. 1 kilogram = 2.2 pounds
How many kilograms are in 140 pounds?

A) 68.64 kg
B) 53.31 kg
C) 71.18 kg
D) 63.64 kg
E) 61.31 kg

Question 37

Solve. Round to the nearest hundredth. $\frac { 31 } { n } = \frac { 19 } { 5 }$

A) 19.00
B) 3.80
C) 6.20
D) 3.06
E) 8.16

Question 38

Write the percent problem as a proportion or equation and solve. Round to the nearest tenth or tenth of a percent. What number is 80% of 42?

A) 33.6
B) 52.5
C) 190.5
D) 30.5
E) 29.4

Question 39

Solve the unit problem using the conversion information. Use either a proportion or unit analysis. Round to the nearest hundredth. Useful facts:
1 square mile = 640 acres
1 mile = 5280 feet
How many square miles are in 20,000 acres?

A) 790.57
B) 31.25
C) 30.05
D) 34.55
E) 20.48

Question 40

Write the percent problem as a proportion or equation and solve. Round to the nearest tenth or tenth of a percent. 145 is what percent of 215?

A) 311.8%
B) 67.4%
C) 148.3%
D) 68.7%
E) 72.8%

Question 41

Late one evening, a 6 foot person is standing 16 feet from a streetlight. The streetlight is 18 feet tall. How long is the person's shadow?

A) 3 feet
B) 9 feet
C) 8 feet
D) 4 feet
E) 2 feet

Question 42

Find the given trigonometric function of the indicated angle using triangle ABC. sin C, where $a = 7 , b = 21 , c = 29$

A) $\frac { 22 } { 29 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 22 } { 9 }$
D) $\frac { 7 } { 29 }$
E) $\frac { 21 } { 29 }$

Question 43

Use a calculator to evaluate the given trigonometric function. Round the answer to three decimal places as needed. $$\tan \left( 45 ^ { \circ } \right)$$ .

A) $1.732$
B) $3.732$
C) $\text { infinity }$
D) $0.577$
E) $1.000$

Question 44

Find the given trigonometric function of the indicated angle using triangle ABC. tan A, where $$a = 5 , b = 23 , c = 29$$

A) $\frac { 1 } { 5 }$
B) $\frac { 5 } { 29 }$
C) $\frac { 23 } { 29 }$
D) $\frac { 5 } { 23 }$
E) $\frac { 29 } { 23 }$

Question 45

Find the given trigonometric function of the indicated angle using triangle ABC. sin A, where $a = 2 , b = 24 , c = 29$

A) $\frac { 24 } { 29 }$
B) $\frac { 29 } { 24 }$
C) $\frac { 2 } { 29 }$
D) $\frac { 2 } { 24 }$
E) $\frac { 24 } { 2 }$

Question 46

Find the given trigonometric function of the indicated angle using triangle RAW. tan W, where $$x = 21 , y = 32 , z = 42$$

A) $\frac { 1 } { 2 }$
B) $\frac { 21 } { 16 }$
C) $\frac { 16 } { 21 }$
D) $\frac { 32 } { 21 }$
E) $\frac { 16 } { 11 }$

Question 47

Find the given trigonometric function of the indicated angle using triangle RAW. cos W, where $$x = 23 , y = 32 , z = 46$$

A) $\frac { 23 } { 32 }$
B) $\frac { 23 } { 12 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 23 } { 16 }$
E) $\frac { 16 } { 23 }$

Question 48

A line segment, AC, has point B between A and C. Segment AC is x in length. Let segment AB be of length 12 units. What is an expression for the other segment, BC?

A) 12 - x
B) 12 + x
C) x - 12
D) 1 - 12x
E) 12x - 1

Question 49

A 10-foot parking meter has a 9-foot shadow from a nearby streetlight. The streetlight is 20 feet tall. How far is the streetlight from the parking meter?

A) $19$ ft
B) $17$ ft
C) $20$ ft
D) $18$ ft
E) $16$ ft

Question 50

Use a calculator to evaluate the given trigonometric function. Round the answer to three decimal places as needed. $$\cos \left( 30 ^ { \circ } \right)$$ .

A) $0.866$
B) $0.966$
C) $1.066$
D) $0.766$
E) $0.666$

Question 51

Use a calculator to evaluate the given trigonometric function. Round the answer to three decimal places as needed. $$\sin \left( 30 ^ { \circ } \right)$$ .

A) $0.600$
B) $0.400$
C) $0.700$
D) $0.300$
E) $0.500$

Question 52

Use proportions to find x. Round your answer to one decimal place.

A) 5.8
B) 6.8
C) 1.8
D) 4.8
E) 9.8

Question 53

Find the given trigonometric function of the indicated angle using triangle ABC. cos C, where $a = 8 , b = 18 , c = 25$

A) $\frac { 2 } { 5 }$
B) $\frac { 8 } { 25 }$
C) $\frac { 18 } { 25 }$
D) $\frac { 25 } { 18 }$
E) $\frac { 8 } { 19 }$

Question 54

The shadow of a flagpole at 10 a.m. is 4 feet. The shadow of a 7 foot person is 1.4 feet. How tall is the flagpole?

A) 20 feet
B) 15 feet
C) 18 feet
D) 13 feet
E) 30 feet

Question 55

Find the given trigonometric function of the indicated angle using triangle RAW. tan R, where $$x = 26 , y = 35 , z = 46$$

A) $\frac { 13 } { 23 }$
B) $\frac { 35 } { 26 }$
C) $\frac { 26 } { 35 }$
D) $\frac { 23 } { 13 }$
E) $\frac { 46 } { 35 }$

Question 56

A line segment, AC, has point B between A and C. Segment AC is 12 units in length. Let segment AB be of length x. What is an expression for the other segment, BC?

A) 12 + x
B) 12 - 12x
C) 1 - 12x
D) 1 - x
E) 12 - x

Question 57

Alicia's Construction has been hired to build an access ramp into the county courthouse.The ramp needs to rise 3 feet.Alicia has chosen a building code angle of 5 $^ { \circ }$ .Approximate the horizontal length of the ramp.

A) $33.3$
B) $35.3$
C) $32.3$
D) $36.3$
E) $34.3$

Question 58

Use Proportions to find x, where $a = 5 , b = 7 , c = 3$

A) $10 \frac { 3 } { 2 }$
B) $10 \frac { 2 } { 3 }$
C) $11 \frac { 2 } { 3 }$
D) $10 \frac { 1 } { 2 }$
E) $11 \frac { 1 } { 2 }$

Question 59

Find the given trigonometric function of the indicated angle using triangle RAW. sin W, where $$x = 23 , y = 35 , z = 41$$

A) $\frac { 41 } { 35 }$
B) $\frac { 23 } { 41 }$
C) $\frac { 41 } { 24 }$
D) $\frac { 35 } { 41 }$
E) $\frac { 23 } { 35 }$

Question 60

At 5:00 p.m., a 30-foot tree casts a 134-foot shadow. How long is the shadow of a person who is 5.5 feet tall? Round your answer to one decimal place.

A) 24.0 feet
B) 25.4 feet
C) 23.8 feet
D) 25.0 feet
E) 24.6 feet

Question 61

Andrej has 14 half-dollars and 24 nickels. How much money does Andrej have?

A) $8.25
B) $8.10
C) $8.05
D) $8.00
E) $8.20

Question 62

Does the phrase describe quantity or rate? 5 % boric acid solution

A) quantity
B) rate
C) neither
D) both

Question 63

Does the phrase describe quantity or rate? 10 cents per dime

A) quantity
B) rate
C) both
D) neither

Question 64

Kim has $2,200 invested at 7% interest and $3,200 at 3% interest. Set up a quantity-rate table. Find the average rate (interest rate) for the table by dividing the sum of the Q $\text { . }$ R column by the sum of the quantity column. Round answer to nearest tenth of a percent.

A) 4.6
B) 5.0
C) 3.8
D) 4.2
E) 5.4

Question 65

Does the phrase describe quantity or rate? 10 coins

A) quantity
B) rate
C) neither
D) both

Question 66

One week, Neva works 15 hours on one job at $5.80 per hour. Her second job pays $7.20 per hour. If she needs to average $6.60 per hour, find how many hours she must work at the second job. Round your answer to the nearest hour if necessary.

A) 40
B) 20
C) 17
D) 30
E) no solution

Question 67

Kana drives 3 hours at 40 miles per hour and 2 hours at 16 miles per hour. Set up a quantity-rate table. Find the average rate (miles per hour) for the table by dividing the sum of the Q $\text { . }$ R column by the sum of the quantity column. Round the answer to the nearest whole number.

A) 29 miles per hour
B) 33 miles per hour
C) 30 miles per hour
D) 34 miles per hour
E) 28 miles per hour

Question 68

How many gallons of hot water at 130 degrees would need to be added to a bathtub containing 19 gallons of cold water at 45 degrees to raise the temperature to 101 degrees? Round your answer to the nearest tenth of a gallon if necessary.

A) 35.7 gal
B) 36.7 gal
C) 38.7 gal
D) 40.7 gal
E) 33.7 gal

Question 69

Bruce has 5 hours at a 2.02 GPA from fall quarter, 5 hours at a 1.71 GPA from winter quarter, and 12 hours at 1.85 GPA from spring quarter. Set up a quantity-rate table. Find the average rate (GPA) for the table by dividing the sum of the Q $\text { . }$ R column by the sum of the quantity column. Round answer to the nearest hundredth.

A) 1.82
B) 1.86
C) 1.87
D) 1.89
E) 1.88

Question 70

Abraham buys 2 pounds of grapes at $0.94 per pound, 5 pounds of potatoes at $0.58 per pound, and 4 pounds of broccoli at $0.78 per pound. What is the total cost of his purchase?

A) $7.92
B) $7.94
C) $7.96
D) $7.90
E) $7.98

Question 71

Maria has $12,000 to invest for one year. Investment A pays 7% interest for the year, and investment B pays 10% interest. She invests $\frac { 1 } { 3 }$ of the money at 7% and $\frac { 2 } { 3 }$ of the money at 10%. Find how much she earns.

A) $1,090
B) $1,120
C) $1,100
D) $1,110
E) $1,080

Question 72

Two students have a 3.05 GPA. This semester, each earns a 3.80 GPA on 10 credit hours. Which student will see more improvement in overall GPA: the fourth-year full-time student or the second-year full-time student?

A) second-year student
B) fourth-year student

Question 73

How many credit hours of Cs (at 2 points per credit hour) will raise 23 credit hours at a 1.875 GPA to a 1.93 GPA? Round your answer to the nearest integer if necessary.

A) 18
B) no solution
C) 17
D) 16
E) 21

Question 74

Ninety shares of Mattel stock have been purchased for $15 per share. How many shares of FedEx at $60 per share are needed to raise the average price of all shares to $50 per share? Round your answer to the nearest share if necessary.

A) 315
B) no solution
C) 210
D) 525
E) 394

Question 75

Ingrid, a chemist, has 180 milliliters of nitric acid with a molarity of 18 and 490 milliliters of nitric acid with a molarity of 5. (Molarity is a chemical term; the larger the molarity, the more concentrated the acid.) Set up a quantity-rate table. Find the average rate (molarity) for the table by dividing the sum of the Q $\text {.}$ R column by the sum of the quantity column. Round the answer to the nearest whole number.

A) 16
B) 13
C) 12
D) 8
E) 9