AMC10 2007 B

AMC10 2007 B · Q12

AMC10 2007 B · Q12. It mainly tests Linear equations.

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?

汤姆的年龄是T岁，这也是他三个孩子的年龄之和。T-N年前，他的年龄是当时他们三个孩子年龄之和的两倍。T/N是多少？

(A) 2 2

(B) 3 3

(D) 5 5

(E) 6 6

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Tom’s age $N$ years ago was $T-N$. The sum of his three children’s ages at that time was $T-3N$. Therefore $T-N=2(T-3N)$, so $5N=T$ and $T/N=5$. The conditions of the problem can be met, for example, if Tom’s age is 30 and the ages of his children are 9, 10, and 11. In that case $T=30$ and $N=6$.

答案（D）：汤姆在 $N$ 年前的年龄是 $T-N$。那时他三个孩子的年龄之和是 $T-3N$。因此 $T-N=2(T-3N)$，所以 $5N=T$ 且 $T/N=5$。例如，当汤姆的年龄为 30 岁、孩子们的年龄分别为 9、10、11 岁时，题目条件可以满足。在这种情况下 $T=30$ 且 $N=6$。

Topics

AL.001 Linear equations