AMC8 2008

AMC8 2008 · Q13

AMC8 2008 · Q13. It mainly tests Linear equations, Averages (mean).

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 $100$ pounds or more than $150$ pounds. So the boxes are weighed in pairs in every possible way. The results are $122$, $125$ and $127$ pounds. What is the combined weight in pounds of the three boxes?

哈曼先生需要知道他要邮寄的三个盒子的总重量（磅）。但是，可用的秤不准确，无法称量小于100磅或大于150磅的重量。因此，盒子以每种可能的方式成对称重。结果分别是122、125和127磅。三个盒子的总重量是多少磅？

(A) 160 160

(B) 170 170

(D) 195 195

(E) 354 354

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): Because each box is weighed two times, once with each of the other two boxes, the total $122+125+127=374$ pounds is twice the combined weight of the three boxes. The combined weight is $\frac{374}{2}=187$ pounds.

答案（C）：因为每个箱子被称重两次（分别与另外两个箱子各称一次），总和 $122+125+127=374$ 磅是三个箱子总重量的两倍。三个箱子的总重量为 $\frac{374}{2}=187$ 磅。

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