Question

两年前 Pete 的年龄是他的表妹 Claire 的三倍。再往前两年，Pete 的年龄是 Claire 的四倍。多少年后，他们年龄之比将为 $2:1$ ？

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：1280

解答：

设 Pete 和 Claire 当前年龄分别为 $p$ 和 $c$ 。

题意给出和化简为和令两式相等，得到 $p - 2 = 3(c - 2)$ $p - 4 = 4(c - 4).$ $p = 3c - 4$ $p = 4c - 12.$ $3c - 4 = 4c - 12$ $c = 8.$

因此 $p = 3 \cdot 8 - 4 = 20.$

设还需 $y$ 年，则化简得所以正确答案是 B。 $20 + y = 2(8 + y),$ $20 + y = 16 + 2y$ $y = 4.$

Let $p$ and $c$ be Pete's and Claire's current ages respectively.

Then we have that $p - 2 = 3(c - 2)$ and $p - 4 = 4(c - 4).$ Simplifying both equations gives us $p = 3c - 4$ and $p = 4c - 12.$ Setting them equal, we have $3c - 4 = 4c - 12$ $c = 8.$

This means that $p = 3 \cdot 8 - 4 = 20.$

Now, we need to find the number of years ( $y$ ) until $20 + y = 2(8 + y),$ which gives us $20 + y = 16 + 2y$ $y = 4.$ Thus, B is the correct answer.

2015 AMC 10A 第 8 题

答案：B

难度评级：1280

解答：

其他年份的第 8 题