Official Guide Explanation:
Problem Solving #14

Background

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Solution and Metadata

Question: 14
Page: 154
Difficulty: 5 (Moderate)
Category 1: Word Problems > Mixture Problems >
Category 2: Arithmetic > Descriptive Statistics > Average
Category 3: Arithmetic > Fractions >

Explanation: Weighted average problems can almost always be simplified. With that in mind, set up the question in algebraic terms, but don't do any calculations until you absolutely must. The weighted average formula for this question looks like this: ((8(12(3/8)) + 4(15(1/4)))/12). Since the denominator and each of the coefficients in the numerator are divisible by 4, simplify as follows: ((2(12(3/8)) + 1(15(1/4)))/3). There's still a bit of work involved, but that's much easier. 2(12(3/8)) = 24(3/4), and 24(3/4) + 15(1/4) = 40. Thus, the final answer will be equivalent to (40/3): it's choice (A), 13(1/3).

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