AMC12 2015 A

AMC12 2015 A · Q6

AMC12 2015 A · Q6. It mainly tests Word problems (algebra).

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 $2 : 1$?

两年前，Pete的年龄是他表妹Claire的三倍。再两年前，Pete的年龄是Claire的四倍。多少年后，他们年龄的比例将是 $2 : 1$？

(A) 2 2

(B) 4 4

(D) 6 6

(E) 8 8

Answer

Correct choice: (B)

正确答案：（B）

Solution

Let $p$ be Pete's present age and $c$ Claire's present age. Then $p-2=3(c-2)$ and $p-4=4(c-4)$. Solving these equations gives $p=20$ and $c=8$. Thus Pete is 12 years older than Claire, so the ratio of their ages will be $2:1$ when Claire is 12 years old. That will occur $12-8=4$ years from now.

设 $p$ 为Pete现在的年龄，$c$ 为Claire现在的年龄。那么 $p-2=3(c-2)$ 和 $p-4=4(c-4)$。解这些方程得到 $p=20$ 和 $c=8$。因此Pete比Claire大12岁，当Claire12岁时，他们年龄比例为 $2:1$。那将在 $12-8=4$ 年后发生。

Topics

AL.017 Word problems (algebra)