2007 AMC 10B 第 12 题

Question

Tom 的年龄为

T

岁，也等于他三个孩子年龄之和。

N

年前，他的年龄是当时三个孩子年龄之和的两倍。

\frac{T}{N}

是多少？

Tom’s age is

T

years, which is also the sum of the ages of his three children. His age

N

years ago was twice the sum of their ages then. What is

\frac{T}{N}?

2

3

4

5

6

用

T

和

N

表示

N

年前三个孩子的年龄和。

Express the children’s total age

N

years ago in terms of

T

and

N

T-N=2(T-3N)

。

T-N=2(T-3N)

N

年前 Tom 的年龄为

T-N

，三个孩子年龄之和为

T-3N

。

条件给出

T-N=2(T-3N)

，所以

T-N=2T-6N

，化简为

5N=T

。

因此

\frac{T}{N}=5

。

所以正确答案是 D。

N

years ago Tom’s age was

T-N,

and the sum of his three children’s ages was

T-3N.

The condition gives

T-N=2(T-3N),

so

T-N=2T-6N,

which simplifies to

5N=T.

Therefore

\frac{T}{N}=5.

Thus, the correct answer is D.

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