## Example Questions

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

Flour, eggs, sugar, and chocolate chips are mixed by weight in the ratio of 12 : 5 : 3 : 5, respectively. How many pounds of chocolate chips are there in 75 pounds of the mixture?

18

15

5

25

15

Explanation:

First, add up the four parts of the ratio. This equals 25 parts. These 25 parts make up the 75 pound mixture, which means the 75 pound mixture is composed of 3 times the 25 parts (25x = 75 so x = 3).

This allows you to know that the number of pounds of chocolate chips is 3 times the ratio, i.e. 3 * 5 = 15. The mixture includes 15 pounds of chocolate chips. The answer is 15.

### Example Question #2 : How To Find Proportion

If there are 120 men and women on a committee, and the ratio of men to women is 5 : 1, how many more men are on the committee than women?

96

72

80

100

80

Explanation:

The best approach is to add the numerator and denominator of the ratio (5 + 1 = 6), and then divide the total by that sum (120/6 = 20). This gives you the value for 1 part when the total is divided into 6 parts and, luckily for us, there is only 1 part women for every 5 parts men. Now set up equal ratios: men/women = 5/1 = x/20. Solve for the number of men by cross multiplying (5 * 20 = 1x). So there are 100 men and 20 women, which makes 80 more men than women.

### Example Question #2 : How To Find Proportion

You have a rope of some length, but 2/3rds of it is cut off and thrown away.  1/4th of the remaining rope is cut off and thrown away. What proportion of the original rope remains?

1/6

1/10

1/3

The answer cannot be determined from the given information.

1/4

1/4

Explanation:

If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.

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

If the sum of a, b and c is 400, and a is 1/3 b and b is  1/4 c, what is the value of a?

300

20

25

33

66

25

Explanation:

Explanation: For this type of problem, build an equation that represents the relationships between the quantities and solve for the quantitiy you need. The problem states that b=1/4c and a = 1/3b. Thus, a = 1/3(1/4)c, or 1/12 of c. Now put everything in terms of c, thus 1/12c + 1/4c +c = 400. Now comes the tricky step--combine like terms and create the improper fraction (1/12c + 3/12c + 12/12c = 16/12c). Reduce the fraction to 4/3. So 400 is 4/3 of c. Thus c is 3/4 of 400, or 300. a is 1/12 of 300, or 25.

### Example Question #1 : How To Find Proportion

Erin went to the movies with her friends.  She spent 1/4 of her allowance on movie tickets and 3/5 of the remaining money on popcorn.  If her allowance is $10, how much money remains? Possible Answers:$3.00

$8.50$5.00

$1.50$7.00

$3.00 Explanation: Since she spent 1/4 on the ticket, 3/5 of the remaining 3/4 of the money was spent on popcorn: 3/5 x 3/4 = 9/20. This means 9/20 of the money was spent on popcorn so in total: 1/4 + 9/20 = 14/20 = 7/10 of her money was spent. This leaves 3/10 of her money behind: 3/10x 10 = 3.00. ### Example Question #2 : Proportion / Ratio / Rate Fudge sells at$18.50 for 5 pounds.  What is the cost for 2 pounds?

$5.50$3.70

$6.75$7.40

$9.25 Correct answer:$7.40

Explanation:

Set up a proportion: 18.50/5 = x/2.  Cross multiply and solve for x: 37 = 5x.... x = 7.40.

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

3 men can paint 3 rooms in 3 hours. How long would it take 1 man to paint 1 room?

2.5 hours

1 hour

1.5 hours

2 hours

3 hours

3 hours

Explanation:

It's tempting to pick 1 hour, but that is a trick answer! Picture 3 men each painting 1 room. All 3 of the rooms are done after 3 hours, so each man actually spends 3 hours painting his room, not 1 hour.

### Example Question #1 : How To Find Proportion

Bob can paint a house in 3 hours. If Bob and his friend Ron work together to paint the house, it takes 2 hours. How long would it take Ron to paint the house if he worked alone?

6 hours

5 hours

2 hours

3 hours

4 hours

6 hours

Explanation:

The easiest way to solve this is with a rate formula: 1 / combined time = 1 / Bob's time + 1 / Ron's time.  We know the combined time and Bob's time, so we can solve for Ron's time:

1/2 = 1/3 + 1/Ron's time

1/Ron's time = 1/2 – 1/3 = 1/6

Ron's time = 6 hours

### Example Question #1 : How To Find Proportion Quantity A: Quantity B: Quantity B is greater

The relationship cannot be determined from the information given

The two quantities are equal

Quantity A is greater

The relationship cannot be determined from the information given

Explanation:

Although it seems as though "Quantity B is greater" is the correct answer at first glance, a further analysis indicates that this answer is a trap. If and are negative numbers, such as and , then would be the larger number. Similarly, is larger if both and are positive numbers. Thus, it cannot be determined which variable is larger simply based on the information given.

### Example Question #11 : Proportion / Ratio / Rate

Jane has a collection of coins consisting of pennies, nickels, and dimes in the ratio 6:3:5.

If there are 42 coins in total, how many pennies are in the collection?

18

7

15

9

12

18

Explanation:

First count the total number of parts in the ratio. Then we can set up a proportion representing As the initial ratio shows, there are 6 pennies for every 14 total coins. In the total set, we have X pennies and 42 total coins. Plugging these numbers into the proportion gives .

Finally, we multiply both sides times 42 to isolate x.  ← Previous 1

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