1976 AMC 12 第 29 题

Question

安和芭芭拉在比较年龄时发现：芭芭拉现在的年龄，等于安在某时的年龄；在那时，芭芭拉的年龄，又等于安在更早某时的年龄；而在那个更早的时候，芭芭拉的年龄是安现在年龄的一半。若她们现在的年龄之和为

44

岁，则安的年龄是

Ann and Barbara were comparing their ages and found that Barbara is as old as Ann was when Barbara was as old as Ann had been when Barbara was half as old as Ann is. If the sum of their present ages is

44

years, then Ann’s age is

22

24

25

26

28

答案：B

知识点：年龄问题一次方程逆推法

难度评级：1950

小提示：

设安和芭芭拉现在的年龄分别为

x

和

y

，且

x+y=44

Let Ann’s and Barbara’s present ages be

x

and

y,

with

x+y=44

大提示：

每遇到一个“在某时”，就从两人的年龄中减去同一段经过的时间

Translate each “when” by subtracting the same elapsed time from both ages

解答：

设安和芭芭拉现在的年龄分别为

x

和

y

，并令她们恒定的年龄差为

d=x-y

。在第一个所述时刻，安的年龄为

y

，所以芭芭拉的年龄为

y-d

。在更早的所述时刻，安的年龄为

y-d

，所以芭芭拉的年龄为

y-2d

。最后一句说明这个年龄等于

\frac{x}{2}

。因此

y-2(x-y)=\frac{x}{2}\text{，}

从而

6y=5x

。再结合

x+y=44

，得

x=24

、

y=20

。

所以正确答案是 B。

Let Ann’s and Barbara’s present ages be

x

and

y,

and let their constant age difference be

d=x-y.

At the first referenced time Ann was

y,

so Barbara was

y-d.

At the earlier referenced time Ann was that age

y-d,

so Barbara was

y-2d.

The final clause says this last age was

\frac{x}{2}.

Hence

y-2(x-y)=\frac{x}{2},

which gives

6y=5x.

Together with

x+y=44,

this yields

x=24

and

y=20.

Therefore, the correct answer is B.

1976 AMC 12 第 29 题

答案：B

难度评级：1950

小提示：

大提示：

解答：

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