2007 AMC 10B 第 12 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

12.

Tom 的年龄为 TT 岁,也等于他三个孩子年龄之和。NN 年前,他的年龄是当时三个孩子年龄之和的两倍。求 T/NT/N

Tom's age is TT years, which is also the sum of the ages of his three children. His age NN years ago was twice the sum of their ages then. What is T/N?T/N?

22

33

44

55

66

答案:D
知识点:年龄问题一次方程
难度评级:1290
解答:

NN 年前 Tom 的年龄为 TNT-N,三个孩子年龄之和为 T3NT-3N

条件给出 TN=2(T3N)T-N=2(T-3N),所以 TN=2T6NT-N=2T-6N,化简为 5N=T5N=T

因此 T/N=5T/N=5

所以正确答案是 D

NN years ago Tom's age was TN,T-N, and the sum of his three children's ages was T3N.T-3N.

The condition gives TN=2(T3N),T-N=2(T-3N), so TN=2T6N,T-N=2T-6N, which simplifies to 5N=T.5N=T.

Therefore T/N=5.T/N=5.

Thus, the correct answer is D.

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