AMC 8 2008 Problem 13
AMC8 2008 年第 13 题
方程与不等式★★★☆☆
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?
哈曼太太需要知道他要邮寄的三个箱子的总重量是多少磅。然而，唯一可用的秤对于称量小于 100 磅或大于 150 磅的重物结果并不精确。因此，最后是以两两组合的方式同时称量 2 个箱子，结果是 122，125 和 127 磅。则这三个箱子的总重量是多少磅？
- A.160
- B.170
- C.187
- D.195
- E.354
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
Each box is weighed twice during this, so the combined weight of the three boxes is half the weight of these separate measures:
Using variables , , and to denote the boxes, with . It is obvious that a+b=122 and a+c=125, since these are the two smallest pairs. Subtracting the former equation from the latter results in c-b=3. Additionally, c+b=127. Solving for and gives c=65 and b=62, so we can thus find a=60. Solving 60+62+65=187
We use variables , , and to denote the three boxes. We know that x+y=122, x+z=125, and y+z=127. Note that the order of the variables or equations doesn't matter as long as they are consistent. By adding all three equations, we obtain 2x+2y+2z=122+125+127=374. Dividing be 2, we obtain the sum x+y+z is 187.
继续练习