SAT Math : How to find a ratio

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #23 : Fractions

A cafeteria with 40 tables can sit 600 people. Some tables can sit 10 people and some can sit 20 people. What is the ratio of the number of 10-person tables to the number of 20-person tables?

Possible Answers:

2:1

1:1

1:2

4:1

1:4

Correct answer:

1:1

Explanation:

Let x be the number of 10-person tables, and y be the number of 20-person tables. Since there are 40 tables in the cafeteria, x + y = 40. 10x represents the number of people sitting at 10-person tables, and 20y represents the number of people sitting at 20-person tables. Since the cafeteria can seat 600 people, 10x + 20y = 600. Now we have 2 equations and 2 unknowns, and can solve the system. To do this, multiply the first equation by 10 and subtract it from the second equation. This yields 0x + 10y = 200; solving for y tells us there are 20 tables that seat 20 people. Since x + y = 40, x = 20, so there are 20 tables that seat 10 people. The ratio of x:y is therefore 1:1.

Example Question #24 : Fractions

The first term in a sequence is m. If every term thereafter is 5 greater than 1/10 of the preceding term, and m≠0, what is the ratio of the second term to the first term?

Possible Answers:

(m+10)/5

(m+5)/10

(m+50)/10m

(m+10)/50m

Correct answer:

(m+50)/10m

Explanation:

The first term is m, so the second term is m/10+5 or (m+50)/10. When we take the ratio of the second term to the first term, we get (((m+50)/10))/m, which is ((m+50)/10)(1/m), or (m+50)/10m.

Example Question #1 : Arithmetic

Two cars were traveling 630 miles. Car A traveled an average speed of 70 miles per hour. If car B traveled 90 miles an hour, how many miles had car A traveled when car B arrived at the destination?

 

Possible Answers:

700

630

490

140

Correct answer:

490

Explanation:

We first divide 630 miles by 90 miles per hour to get the amount of time it took car B to reach the destination, giving us 7 hours. We then multiply 7 hours by car A’s average speed and we get 490 miles.

 

 

Example Question #1 : How To Find A Ratio

STUDENT ATHLETES WHO USE STEROIDS

 

MEN

WOMEN

TOTAL

BASKETBALL

A

B

C

SOCCER

D

E

F

TOTAL

G

H

I

 

 

 

 

 

 

In the table above, each letter represents the number of students in each category. Which of the following must be equal to I?

 

Possible Answers:

A+D+G

G+H

A+D

A+B

Correct answer:

G+H

Explanation:

Since G is the total number of male athletes that use steroids and H is the total number of female athletes that use steroids, the sum of the two is equal to I, which is the total number of all students using steroids.

Example Question #3 : Arithmetic

A particular ball always bounces back to 2/5 of the height of its previous bounce after being dropped. After the first bounce it reaches a height of 175 inches. Approximately how high (in inches) will it reach after its fifth bounce?

Possible Answers:

4.5

20

14

11.2

Correct answer:

4.5

Explanation:

The first bounce reaches a height of 175. The second bounce will equal 175 multiplied by 2/5 or 70. Repeat this process. You will get the data below. 4.48 is rounded to 4.5.

Example Question #2 : Proportion / Ratio / Rate

A lawn can be mowed by 8 people in 6 hours. If 3 people take the day off and do not help mow the grass, how many hours will it take to mow the lawn?

Possible Answers:

9 and 3/5

6 and 2/5

2 and 1/4

5 and 1/2

12 and 1/8

Correct answer:

9 and 3/5

Explanation:

The number of hours required to mow the lawn remains constant and can be found by taking the original 8 workers times the 6 hours they worked, totaling 48 hours. We then split the total required hours between the 5 works that remain, and each of them have to work 9 and 3/5 hours: 48/5 = 9 and 3/5.

Example Question #4 : Proportion / Ratio / Rate

The flow of water through a certain pipe is 20 cubic meters per minute.  How many minutes would it take for 4 of such pipes to fill 2 tanks, if each tank is a cube with a side length of 20 m?

Possible Answers:

50

40

200

20

100

Correct answer:

200

Explanation:

The flow of water through one pipe is 20 m/ minute.

Thus, the flow of water through 4 pipes is 80 m3 / minute.

Since each tank is a cube with a side length of 20m, the volume of each tank is:

Volume of one tank = (20 m)3 = 8000 m3.

The total volume of two tanks is 2 * 8000 m= 16,000 m3

 

Therefore, the total minutes for 4 pipes to fill 2 tanks is:

16,000 m3/(80 m3/min) = 200 minutes

80 m3/min

Example Question #4 : Proportion / Ratio / Rate

You are planning a party.  The maximum number of people the reception hall can hold is 1 person for every 5 square feet of space.  If the hall is 60 feet wide and 50 feet long, how many people can you invite?

Possible Answers:

500

1500

2500

3000

600

Correct answer:

600

Explanation:

Total area of hall = 60ft * 50ft = 3000 ft2

At 1 person per 5 square feet, 3000 ft2 / 5 ft2 per person  = 600 people

Example Question #1 : Proportion / Ratio / Rate

A gallon contains 8 pints.  Each pint contains 2 cups.  How many cups are in a 10-gallon jug of water?

Possible Answers:

220

160

26

80

20

Correct answer:

160

Explanation:

Find the number of cups in a gallon, then calculate cups in 10 gallons.

If 8 pints = 1 gallon, then 16 cups = 1 gallon

16 cups * 10 gallons = 160 cups

Example Question #2 : How To Find A Ratio

A mile is 5280 feet

Susan is able to walk a fast pace of 4 miles per hour.  How many feet will she walk in 40 minutes?

Possible Answers:

8/3

15840

14080

3

15000

Correct answer:

14080

Explanation:

Calculate the number of feet walked in an hour.  Then calculate what fraction of an hour 40 minutes is.

5280 * 4 = 21120 feet walked in an hour

60 minutes in an hour, so 40 minutes = 2/3 hour (40/60)

21120(2/3) = 14080 feet walked in 40 minutes

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