Official Guide Explanation:
Problem Solving #107




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Solution and Metadata

Question: 107
Page: 75
Difficulty: 5 (Moderate)
Category 1: Algebra > Simplifying Algebraic Expressions >
Category 2: Algebra > Linear Equations-One Unk >

Explanation: It may look like the two fractions (3/(x)) and ((y)/4) can be added to create ((3 + y)/(x + 4)), but they can't, not without a common denominator. Instead, solve each of the first two equations for the variable in each, then plug in to ((3 + y)/(x + 4)):

(3/(x)) = 2

2x = 3

x = (3/2)

((y)/4) = 3

y = 12

((3 + y)/(x + 4)) = ((3 + 12)/((3/2) + 4)) = (15/((3/2) + (8/2))) = (15/((11/2))) = 15((2/11)) = (30/11), choice (D).

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