Official Guide Explanation:
Problem Solving #66

Background

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Solution and Metadata

Question: 66
Page: 161
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Ratio and Proportion >

Explanation: This question gives us three ratios and asks us to combine them to generate a fourth. There are a total of four variables: The number of first, second, third, and fourth graders. To avoid the confusion of "first" and "fourth" starting with the same letter, call the variables a, b, c, and d, respectively.

Here are the given ratios:

b:d = 8:5

a:b = 3:4

c:d = 3:2

We're looking for a:c.

Combining ratios is much like finding common denominators. To combine the first two, we'll need the value for b to be the same. If a:b = 3:4, the ratio is equivalent to 6:8. Now the first two ratios have the same value of b, 8. Thus, the ratio of a:b:d = 6:8:5, or:

a:d = 6:5

Now, to relate a and c, combine this new ratio with c:d = 3:2. Since d is the common term, multiply each ratio so that d = 10:

a:d = 12:10

c:d = 15:10

Now, a:d:c = 12:10:15, or a:c = 12:15, which simplifies to 4:5, choice (E).

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