Official Guide Explanation:
Problem Solving #204

Background

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Solution and Metadata

Question: 204
Page: 181
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Work Problems > 2 inputs
Category 3: Word Problems > Rate Problems > other

Explanation: If John and Mary were each paid x dollars, and worked 10 and (10 - 2) = 8 hours, respectively, their hourly rates were as follows. John's was: ((x)/10), and Mary's was ((x)/8). If Mary gave John y dollars of her payment, their respective rates were ((x + y)/10) and ((x - y)/8). Since those are equal, we can set up an equation to solve for x in terms of y:

((x + y)/10) = ((x - y)/8)

10(x - y) = 8(x + y)

10x - 10y = 8x + 8y

2x = 18y

x = 9y

We're looking for the amount John was paid in advance, which is equal to x, so the answer is 9y, choice (E).

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