Official Guide Explanation:
Problem Solving #154




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Solution and Metadata

Question: 154
Page: 82
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Mixture Problems >
Category 2: Arithmetic > Descriptive Statistics > Average
Category 3: Arithmetic > Percents > Percent Change

Explanation: This is essentially a weighted average question. We need to figure out what "weight" is assigned to salary costs and fringe - benefit costs. We're given an equation, where s is salary costs and f is fringe - benefit costs.

3.5(s + f) = 3s + 5.5f

We want the relationship between f and s + f. Simplify:

3.5s + 3.5f = 3s + 5.5f

0.5s = 2f

s = 4f

In other words, s has four times the weight of f. We're looking for ((f)/(s + f)), so substitute:

((f)/(s + f)) = ((f)/((4f) + f)) = ((f)/(5f)) = (1/5) = 20%, choice (B).

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