AMC12 2007 B

AMC12 2007 B · Q8

AMC12 2007 B · Q8. It mainly tests Systems of equations, Arithmetic misc.

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 $T/N$?

Tom 的年龄是 $T$ 岁，这也是他三个孩子的年龄之和。$N$ 年前，他的年龄是当时他们年龄之和的两倍。$T/N$ 等于多少？

(A) 2 2

(B) 3 3

(D) 5 5

(E) 6 6

Answer

Correct choice: (D)

正确答案：（D）

Solution

Tom's age $N$ years ago was $T-N$. The sum of the ages of his three children $N$ years ago was $T-3N,$ since there are three children. If his age $N$ years ago was twice the sum of the children's ages then, \begin{align*}T-N&=2(T-3N)\\ T-N&=2T-6N\\ T&=5N\\ T/N&=\boxed{\mathrm{(D) \ } 5}\end{align*} Note that actual values were not found.

Tom 在 $N$ 年前的年龄是 $T-N$。他三个孩子在 $N$ 年前的年龄之和是 $T-3N,$ 因为有三个孩子。若 Tom 在 $N$ 年前的年龄是当时孩子们年龄之和的两倍，则 \begin{align*}T-N&=2(T-3N)\\ T-N&=2T-6N\\ T&=5N\\ T/N&=\boxed{\mathrm{(D) \ } 5}\end{align*} 注意不需要求出具体数值。

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