Question

Harman 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 $100$ 磅或大于 $150$ 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 $122$ 、 $125$ 和 $127$ 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 $100$ 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?

$\ 160$

$\ 170$

$\ 187$

$\ 195$

$\ 354$

答案：C

知识点：方程组

难度评级：1060

解答：

设三个箱子的重量为 $a,b,c$ 已知把这些式子相加得到所以 $\begin{cases}a+b = 122\\a+c = 125\\b+c = 127.\end{cases}$ $2(a+b+c) =$ $122+125+127=374.$ $a+b+c = 187.$

所以正确答案是 C。

Let the weights be $a,b,c.$ We know $\begin{cases}a+b = 122\\a+c = 125\\b+c = 127.\end{cases}$ Adding all of this yields $2(a+b+c) =$ $122+125+127=374.$ This makes $a+b+c = 187.$

Thus, the answer is C .

2008 AMC 8 第 13 题

答案：C

难度评级：1060

解答：

其他年份的第 13 题