2015 AMC 10A 第 8 题

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

小提示：

用当前年龄翻译两个年龄关系。

Translate the two age statements using current ages

大提示：

先求出当前年龄，再列出未来的年龄比。

Solve for current ages before setting the future ratio

解答：

设 Pete 和 Claire 当前年龄分别为

p

和

c

。

题意给出

p - 2 = 3(c - 2)

和

p - 4 = 4(c - 4)\text{。}

化简为

p = 3c - 4

和

p = 4c - 12\text{。}

令两式相等，得到

3c - 4 = 4c - 12

c = 8\text{。}

因此

p = 3 \cdot 8 - 4 = 20\text{。}

设还需

y

年，则

20 + y = 2(8 + y)\text{，}

化简得

20 + y = 16 + 2y

y = 4\text{。}

所以正确答案是 B。

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

小提示：

大提示：

解答：

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