2008 AMC 8 第 13 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。
13.
哈曼先生想知道他要邮寄的三个箱子的总重量，单位为磅。不过唯一可用的秤在重量小于 磅或大于 磅时不准确。于是他把箱子按所有可能的两两组合称重，结果是 、 和 磅。这三个箱子的总重量是多少磅？
Mr. Harman needs to know the combined weight in pounds of three boxes he wants to mail. However, the only available scale is not accurate for weights less than pounds or more than pounds. So the boxes are weighed in pairs in every possible way. The results are and pounds. What is the combined weight in pounds of the three boxes?
答案：C
小提示：
三个两箱重量之和中，每个箱子都恰好出现两次
Each box appears in exactly two of the three pair weights.
大提示：
把三个两箱重量相加，再除以
Add the three pair weights, then divide by
解答：
设三个箱子的重量为 、、。已知 把这些式子相加得到 所以
所以正确答案是 C。
Let the weights be We know Adding all of this yields This makes
Thus, the answer is C .
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