1999 AMC 12 第 8 题

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

小提示：

设 Walter 在

1994

年底为

w

岁，他祖母为

2w

岁。

Let Walter be

w

and his grandmother

2w

at the end of

1994

大提示：

他们的出生年份分别为

1994 - w

和

1994 - 2w

Their birth years are

1994 - w

and

1994 - 2w

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

\begin{aligned} &(1994 - w) \\ &\quad {}+ (1994 - 2w) = 3838\text{。} \end{aligned}

因此

3988 - 3w = 3838

，得

w = 50

。

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

小提示：

大提示：

解答：

其他年份的第 8 题