AMC10 2015 A
AMC10 2015 A · Q8
AMC10 2015 A · Q8. 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，皮特的年龄是他的表妹克莱尔的三倍。再往前两年，皮特的年龄是克莱尔的四倍。再过多少年，他们的年龄之比将是$2:1$？
(A)
2
2
(B)
4
4
(C)
5
5
(D)
6
6
(E)
8
8
Answer
Correct choice: (B)
正确答案：（B）
Solution
Answer (B): Let $p$ be Pete's present age, and let $c$ be Claire's 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.
答案（B）：设 $p$ 为 Pete 现在的年龄，设 $c$ 为 Claire 的年龄。则有 $p-2=3(c-2)$ 且 $p-4=4(c-4)$。解这两个方程得 $p=20$，$c=8$。因此 Pete 比 Claire 大 12 岁，所以当 Claire 12 岁时，他们年龄之比为 $2:1$。这将在从现在起 $12-8=4$ 年后发生。
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