## Example Questions

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### Example Question #1 : Proportion / Ratio / Rate

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?

1:2

1:4

1:1

4:1

2:1

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 #2 : Proportion / Ratio / Rate

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?

(m+50)/10m

(m+10)/5

(m+10)/50m

(m+5)/10

(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 #3 : Proportion / Ratio / Rate

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?

630

140

490

700

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 #4 : Proportion / Ratio / Rate

 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?

A+B

A+D

A+D+G

G+H

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 #5 : Proportion / Ratio / Rate

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?

20

4.5

14

11.2

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 #6 : 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?

50

40

200

20

100

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 #1 : 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?

1500

600

2500

3000

500

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 #8 : Proportion / Ratio / Rate

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

20

26

220

160

80

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 #9 : Proportion / Ratio / Rate

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?

14080

15000

15840

3

8/3

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

### Example Question #10 : Proportion / Ratio / Rate

Two numbers have a ratio of 5 : 2. If they are positive and differ by 21, what is the value of the larger number?

14

35

70

28

35

Explanation:

We can rewrite this as two equations

5/2 = x/y

x – y = 21

Solve y for x in the second equation: x = 21 + y → y = x – 21

Substitute back into the first equation and solve:

5/2 = x/(x – 21)

5(x – 21)/2 = x → (5x – 105)/2 = x → 5x – 105 = 2x → 5x – 2x = 105 → 3x = 105; x = 105/3 = 35

Since we know the numerator must be larger (given the prompt), the answer is x, or 35.

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