2015 AMC 12A Problem 6

Problem 6 of 25EasierAlgebra

Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be

2 : 1?

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Solution

Let

p

and

c

be Pete’s and Claire’s current ages. Then

p-2 = 3(c-2)

and

p-4 = 4(c-4).

Solving these gives

p = 20

and

c = 8,

so Pete is

12

years older than Claire. The ratio is

2 : 1

when Claire is

12,

which is

12 - 8 = 4

years from now. Thus, the correct answer is B.

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