2015 AMC 12A 第 6 题

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

小提示：

设

p,c

为他们现在的年龄：

p-2=3(c-2)

且

p-4=4(c-4)

Let

p,c

be their current ages:

p-2=3(c-2)

and

p-4=4(c-4)

大提示：

先求出

p

和

c

，再找满足

p+n = 2(c+n)

的

n

。

Solve for

p

and

c,

then find

n

with

p+n = 2(c+n)

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

小提示：

大提示：

解答：

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