Question

两年前，Pete 的年龄是他的堂妹 Claire 的三倍。再往前两年，Pete 的年龄是 Claire 的四倍。多少年后，他们年龄的比会是 $2 : 1$ ？

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 $2 : 1?$

$2$

$4$

$5$

$6$

$8$

答案：B

知识点：年龄问题方程组

难度评级：1350

解答：

设 $p$ 和 $c$ 分别为 Pete 和 Claire 现在的年龄。则 $p-2 = 3(c-2)$ 且 $p-4 = 4(c-4)$ 。

解得 $p = 20$ 且 $c = 8$ ，所以 Pete 比 Claire 大 $12$ 岁。

当 Claire 为 $12$ 岁时，年龄比为 $2 : 1$ ，这距离现在还有 $12 - 8 = 4$ 年。

因此，正确答案是 B。

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.

2015 AMC 12A 第 6 题

答案：B

难度评级：1350

解答：

其他年份的第 6 题