Question 1

Use a proportion to solve the problem.
-On a map, the length of a nature-center trail is 9.2 centimeters. If the scale is 2 centimeters to 21 kilometers, what is the actual length of the trail?
A) $100.6 \mathrm{~km}$
B) $193.2 \mathrm{~km}$
C) $97.6 \mathrm{~km}$
D) $96.6 \mathrm{~km}$

Accepted Answer

The proportion is set up as $ \frac{2 \text{ cm}}{21 \text{ km}} = \frac{9.2 \text{ cm}}{x \text{ km}} $. Solving for $ x $, we get $ x = \frac{9.2 \times 21}{2} = 96.6 \text{ km} $.

Question 2

Use a proportion to solve the problem.
-Joan can mow a 7 -acre field in 4 hours. How long would it take her to mow a 4.9 -acre field?
A) $0.7 \mathrm{hr}$
B) $4.8 \mathrm{hr}$
C) $5.8 \mathrm{hr}$
D) $2.8 \mathrm{hr}$

Accepted Answer

Joan mows at a rate of 7 acres/4 hours, so for a 4.9-acre field: $4.9 \text{ acres} \times \frac{4 \text{ hours}}{7 \text{ acres}} = 2.8 \text{ hours}$.

Question 3

Use a proportion to solve the problem.
-A label printer prints 2 pages of labels in 2.9 seconds. How long will it take to print 6 pages of labels?
A) $8.70 \mathrm{sec}$
B) $10.70 \mathrm{sec}$
C) $12.70 \mathrm{sec}$
D) $11.70 \mathrm{sec}$

Accepted Answer

The time to print pages of labels is directly proportional to the number of pages. If 2 pages take 2.9 seconds, then 6 pages will take $6 \times \frac{2.9}{2} = 8.7$ seconds.

Question 4

Use a proportion to solve the problem.
-If 7 sandwich rolls cost $\$ 1.82$, how much will 25 rolls cost?
A) $\$ 12.74$
B) $\$ 7.50$
C) $\$ 14.74$
D) $\$ 6.50$

Accepted Answer

The answer of Use a proportion to solve the problem.
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Question 5

Use a proportion to solve the problem.
-Jim drove 144 miles in 4 hours. If he can keep the same pace, how long will it take him to drive 432 miles?
A) $22 \mathrm{hr}$
B) $24 \mathrm{hr}$
C) $12 \mathrm{hr}$
D) $576 \mathrm{hr}$

Accepted Answer

Jim's driving rate is 144 miles in 4 hours, which simplifies to 36 miles per hour. To find out how long it takes to drive 432 miles at this rate, divide 432 by 36, which equals 12 hours.

Question 6

Use a proportion to solve the problem.
-If a spring stretches 5 meters when a 2 -kilogram weight is attached to it, how much will it stretch when a 16-kilogram weight is attached to it?
A) $40 \mathrm{~m}$
B) $39 \mathrm{~m}$
C) $42 \mathrm{~m}$
D) $43 \mathrm{~m}$

Accepted Answer

The stretch of the spring is directly proportional to the weight attached to it. So, if 2 kilograms cause a 5-meter stretch, 16 kilograms (which is 8 times more weight) will cause an 8 times greater stretch: $5 \mathrm{~m} \times 8 = 40 \mathrm{~m}$.

Question 7

Use a proportion to solve the problem.
-On Anne's bicycle, the ratio of pedal turns to rear-wheel turns in second gear is 4 to 7 . If her rear wheel turns 833 times per mile, how many times does she turn the pedal in one mile?
A) 837 times
B) 840 times
C) 1457.8 times
D) 476 times

Accepted Answer

The answer of Use a proportion to solve the problem.
-On...

Question 8

Use a proportion to solve the problem.
-The ratio of the lengths of strings that play the notes $F$ and $G$ is 9 to 8 . If a string 56 centimeters long plays a $\mathrm{G}$, what is the length of the string that plays an $\mathrm{F}$ ?
A) $64 \mathrm{~cm}$
B) $49.8 \mathrm{~cm}$
C) $65 \mathrm{~cm}$
D) $63 \mathrm{~cm}$

Accepted Answer

The ratio of the lengths of strings for notes F and G is 9 to 8. Given a G string length of 56 cm, we set up the proportion 9/8 = x/56, where x is the length of the F string. Solving for x gives x = (9/8) * 56 = 63 cm.

Question 9

Use a proportion to solve the problem.
-The ratio of the distances a 7 -iron and a 5 -iron will drive a golf ball is 5 to 6 . If a golfer averages 166 yards with a 7 -iron, how far should he average with a 5 -iron?
A) $138 \mathrm{yd}$
B) $155 \mathrm{yd}$
C) $199.2 \mathrm{yd}$
D) $177 \mathrm{yd}$

Accepted Answer

The ratio of the distances is 5:6, so if the 7-iron drives 166 yards (corresponding to 5 parts), the 5-iron (corresponding to 6 parts) should drive $166 \times \frac{6}{5} = 199.2$ yards.

Question 10

Use a proportion to solve the problem.
-On a map of the Thunderbird Country Club golf course, 2.5 inches represent 30 yards. How long is the 11th hole if the map shows 16.5 inches?
A) $4.5 \mathrm{yd}$
B) $198 \mathrm{yd}$
C) $1237.5 \mathrm{yd}$
D) $495 \mathrm{yd}$

Accepted Answer

The proportion based on the given information is $2.5 \text{ inches} : 30 \text{ yards} = 16.5 \text{ inches} : x \text{ yards}$. Solving for $x$ gives $x = \frac{30 \times 16.5}{2.5} = 198$ yards.

Question 11

Use a proportion to solve the problem.
-The scale on a map is $\frac{1}{4}$ inch to 6 miles. Find the actual distance between two towns for which the distance is represented by 32 inches on the map.
A) $756 \mathrm{mi}$
B) $771.85 \mathrm{mi}$
C) $760.5 \mathrm{mi}$
D) $768 \mathrm{mi}$

Accepted Answer

The scale is $\frac{1}{4}$ inch to 6 miles, so for every $\frac{1}{4}$ inch on the map, the actual distance is 6 miles. For 32 inches on the map, the actual distance is $32 \times \frac{6}{\frac{1}{4}} = 32 \times 24 = 768$ miles.

Question 12

Use a proportion to solve the problem.
-On a map of the Fox River, 1 centimeter represents 2.5 kilometers. If a trail by the river is actually 10.00 kilometers long, what is the length of the trail on the map?
A) $2.5 \mathrm{~cm}$
B) $4.0 \mathrm{~cm}$
C) $6 \mathrm{~cm}$
D) $7.5 \mathrm{~cm}$

Accepted Answer

The proportion based on the given information is $1 \mathrm{~cm} / 2.5 \mathrm{~km} = x \mathrm{~cm} / 10.00 \mathrm{~km}$. Solving for $x$ gives $x = (10.00 \mathrm{~km} \times 1 \mathrm{~cm}) / 2.5 \mathrm{~km} = 4.0 \mathrm{~cm}$.

Question 13

Use a proportion to solve the problem.
-The 6th hole at the Riverwoods Golf Course is 375 yards long. How long would it be on a model with a scale of 2.5 inches to 75 yards?
A) 12.5 in.
B) 93.75 in.
C) 187.5 in.
D) 6.25 in.

Accepted Answer

The scale is 2.5 inches for every 75 yards. To find the length on the model, set up a proportion: (2.5 inches / 75 yards) = (x inches / 375 yards). Solving for x gives x = (2.5 * 375) / 75 = 12.5 inches.

Question 14

Use a proportion to solve the problem.
-In the rectangles below, the ratio of length to width is the same. Find the length of the larger rectangle.

A) $39 \mathrm{ft}$
B) $48 \mathrm{ft}$
C) $45 \mathrm{ft}$
D) $42 \mathrm{ft}$

Accepted Answer

The answer of Use a proportion to solve the problem.
-In...

Question 15

Use a proportion to solve the problem.
-To determine the number of fish in a lake, a park ranger catches 240 fish, tags them, and returns them to the lake. Later, 72 fish are caught, and it is found that 20 of them are tagged. Estimate the number of fish in the lake.
A) 6 fish
B) 345,600 fish
C) 864 fish
D) 67 fish

Accepted Answer

The proportion of tagged fish in the sample (20 out of 72) should be equal to the proportion of all tagged fish in the lake (240 out of the total number of fish). Setting up the proportion 20/72 = 240/x and solving for x gives x = 864, estimating the total number of fish in the lake.

Question 16

Use a proportion to solve the problem.
-A quality-control inspector examined 190 calculators and found 11 of them to be defective. At this rate, how many defective calculators will there be in a batch of 15,960 calculators?
A) 8 calculators
B) 2090 calculators
C) 84 calculators
D) 924 calculators

Accepted Answer

The proportion of defective calculators is 11/190. To find the number of defective calculators in a batch of 15,960, set up the proportion 11/190 = x/15960 and solve for x. This gives x = (11 * 15960) / 190 = 924.

Question 17

Use a proportion to solve the problem.
-Under typical conditions, $1 \frac{1}{2} \mathrm{ft}$ of snow will melt to 2 in. of water. To how many inches of water will $5 \frac{1}{2} \mathrm{ft}$ of snow melt?
A) $7 \frac{1}{3}$ in.
B) $7 \frac{1}{2} \mathrm{in}$.
C) 11 in.
D) $8 \frac{1}{4}$ in.

Accepted Answer

To solve the problem, set up a proportion using the given information: $\frac{1.5 \text{ ft of snow}}{2 \text{ in. of water}} = \frac{5.5 \text{ ft of snow}}{x \text{ in. of water}}$. Solving for $x$ gives $x = \frac{5.5 \times 2}{1.5} = 7.333$ inches of water, which is $7 \frac{1}{3}$ inches.

Question 18

Use a proportion to solve the problem.
-The prize money in a competition will be divided between the $3 \mathrm{rd}$, 2nd, and 1st place winners as $1: 2: 4$. That is, the second place winner will receive 2 times as much as the third place winner and the first place winner will receive 4 times as much as the third place winner. If the total amount of prize money is $\$ 3500$, how should the money be divided among the three winners?
A) 3rd place: $\$ 500,2$ nd place: $\$ 1000$, 1st place: $\$ 2000$
B) 3rd place: $\$ 778$, 2nd place: $\$ 1167,1$ st place: $\$ 1556$
C) 3rd place: $\$ 438$, 2nd place: $\$ 875$, 1st place: $\$ 1750$
D) 3rd place: $\$ 583$, 2nd place: $\$ 1167,1$ st place: $\$ 2333$

Accepted Answer

The total prize money ratio is $1 + 2 + 4 = 7$ parts. Therefore, each part is $\$3500 / 7 = \$500$. Thus, 3rd place gets \$500, 2nd place gets $2 \times \$500 = \$1000$, and 1st place gets $4 \times \$500 = \$2000$.

Question 19

Use a proportion to solve the problem.
-In baseball, the average number of earned runs given up by a pitcher in 9 innings is the pitcher's earned run average, ERA. For example, if a player gave up 90 earned runs in 250 innings during one year, his ERA is found by solving the proportion $\frac{\text { ERA }}{9}=\frac{90}{250}$. Find the ERA for a player who, in one year, gave up 101 earned runs in 239 innings. Round your answer to the nearest hundredth.
A) 3.80
B) 2.37
C) 21.30
D) 11.22

Accepted Answer

To find the ERA, set up the proportion $\frac{\text{ERA}}{9} = \frac{101}{239}$ and solve for ERA. Multiplying both sides by 9 gives $\text{ERA} = \frac{101}{239} \times 9$, which calculates to approximately 3.80 when rounded to the nearest hundredth.

Question 20

Use a proportion to solve the problem.
-A math teacher claims that the students' test scores are directly proportional to the amount of time spent studying. Amy studies 14 hours for a test and gets a score of 70 . At this rate, how many hours would she have to study to get a score of 83 ?
A) $27 \mathrm{hr}$
B) $17.43 \mathrm{hr}$
C) $16.6 \mathrm{hr}$
D) $11.81 \mathrm{hr}$

Accepted Answer

The answer of Use a proportion to solve the problem.
-A...

Quiz 4: Percent Notation

Use a proportion to solve the problem. -On a map, the length of a nature-center trail is 9.2 centimeters. If the scale is 2 centimeters to 21 kilometers, what is the actual length of the trail?

Use a proportion to solve the problem. -Joan can mow a 7 -acre field in 4 hours. How long would it take her to mow a 4.9 -acre field?

Use a proportion to solve the problem. -A label printer prints 2 pages of labels in 2.9 seconds. How long will it take to print 6 pages of labels?

Use a proportion to solve the problem. -If 7 sandwich rolls cost $\$ 1.82$ , how much will 25 rolls cost?

Use a proportion to solve the problem. -Jim drove 144 miles in 4 hours. If he can keep the same pace, how long will it take him to drive 432 miles?

Use a proportion to solve the problem. -If a spring stretches 5 meters when a 2 -kilogram weight is attached to it, how much will it stretch when a 16-kilogram weight is attached to it?

Use a proportion to solve the problem. -On Anne's bicycle, the ratio of pedal turns to rear-wheel turns in second gear is 4 to 7 . If her rear wheel turns 833 times per mile, how many times does she turn the pedal in one mile?

Use a proportion to solve the problem. -The ratio of the lengths of strings that play the notes $F$ and $G$ is 9 to 8 . If a string 56 centimeters long plays a $\mathrm{G}$ , what is the length of the string that plays an $\mathrm{F}$ ?

Use a proportion to solve the problem. -The ratio of the distances a 7 -iron and a 5 -iron will drive a golf ball is 5 to 6 . If a golfer averages 166 yards with a 7 -iron, how far should he average with a 5 -iron?

Use a proportion to solve the problem. -On a map of the Thunderbird Country Club golf course, 2.5 inches represent 30 yards. How long is the 11th hole if the map shows 16.5 inches?

Use a proportion to solve the problem. -The scale on a map is $\frac{1}{4}$ inch to 6 miles. Find the actual distance between two towns for which the distance is represented by 32 inches on the map.

Use a proportion to solve the problem. -On a map of the Fox River, 1 centimeter represents 2.5 kilometers. If a trail by the river is actually 10.00 kilometers long, what is the length of the trail on the map?

Use a proportion to solve the problem. -The 6th hole at the Riverwoods Golf Course is 375 yards long. How long would it be on a model with a scale of 2.5 inches to 75 yards?

Use a proportion to solve the problem. -To determine the number of fish in a lake, a park ranger catches 240 fish, tags them, and returns them to the lake. Later, 72 fish are caught, and it is found that 20 of them are tagged. Estimate the number of fish in the lake.

Use a proportion to solve the problem. -A quality-control inspector examined 190 calculators and found 11 of them to be defective. At this rate, how many defective calculators will there be in a batch of 15,960 calculators?

Use a proportion to solve the problem. -Under typical conditions, $1 \frac{1}{2} \mathrm{ft}$ of snow will melt to 2 in. of water. To how many inches of water will $5 \frac{1}{2} \mathrm{ft}$ of snow melt?

Use a proportion to solve the problem. -A math teacher claims that the students' test scores are directly proportional to the amount of time spent studying. Amy studies 14 hours for a test and gets a score of 70 . At this rate, how many hours would she have to study to get a score of 83 ?