Official Guide Explanation:
Problem Solving #115




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Solution and Metadata

Question: 115
Page: 76
Difficulty: 5 (Moderate)
Category 1: Algebra > Linear Equations-Two Unk >
Category 2: Algebra > Equations >

Explanation: This question throws you a curve with the addition of y to Fred's age at the end, but until that point, it's very much the other questions you've seen with two people's ages. As usual, translate each statement into algebra:

d + f = y

d = f + 12

Then substitute one equation into the other, and solve:

(f + 12) + f = y

2f + 12 = y

2f = y - 12

f = ((y - 12)/2)

Now that Fred's age is established in terms of y, add the "y years from now:"

f + y = ((y - 12)/2) + y = ((y - 12)/2) + ((2y)/2) = ((y - 12 + 2y)/2) = ((3y - 12)/2) = ((3y)/2) - (12/2) = ((3y)/2) - 6, choice (D).

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