Question

在 $1994$ 年底，Walter 的年龄是他祖母年龄的一半。他们出生年份之和为 $3838$ 。到 $1999$ 年底，Walter 几岁？

At the end of $1994$ Walter was half as old as his grandmother. The sum of the years in which they were born is $3838.$ How old will Walter be at the end of $1999?$

$48$

$49$

$53$

$55$

$101$

答案：D

知识点：年龄问题一次方程

难度评级：1240

解答：

设 Walter 在 $1994$ 年底为 $w$ 岁，则祖母为 $2w$ 岁。两人的出生年份为 $1994 - w$ 和 $1994 - 2w$ ，且因此 $3988 - 3w = 3838$ ，得 $w = 50$ 。 $\begin{aligned} &(1994 - w) \\ &\quad {}+ (1994 - 2w) = 3838. \end{aligned}$

到 $1999$ 年底，Walter 年龄为 $50 + 5 = 55$ 。

所以正确答案是 D。

Let Walter be $w$ years old at the end of $1994,$ so his grandmother is $2w.$ Their birth years are $1994 - w$ and $1994 - 2w,$ and $\begin{aligned} &(1994 - w) \\ &\quad {}+ (1994 - 2w) = 3838. \end{aligned}$ This gives $3988 - 3w = 3838,$ so $w = 50.$

At the end of $1999,$ Walter will be $50 + 5 = 55.$

Thus, the correct answer is D.

1999 AMC 12 第 8 题

答案：D

难度评级：1240

解答：

其他年份的第 8 题