AMC 8 2007 Problem 1
AMC8 2007 年第 1 题
统计与数据图表★☆☆☆☆
Theresa's parents have agreed to buy her tickets to see her favorite band if she spends an average of 10 hours per week helping around the house for 6 weeks. For the first 5 weeks she helps around the house for 8 , 11 , 7 , 12 and 10 hours. How many hours must she work for the final week to earn the tickets?
如果特蕾莎平均每周花 10 个小时在家里帮忙，一共帮忙 6 周，那么她的父母就同意给她买票去看她最喜欢的乐队。在最初的 5 周里，她在家里帮忙了 8，11，7，12 和 10 个小时。最后一周她必须工作多少小时才能挣到票？
- A.9
- B.10
- C.11
- D.12
- E.13
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
Let be the number of hours she must work for the final week. We are looking for the average, so Solving gives 48 + x = 60 x = 12 So, the answer is 12.
Use average deviation: The average is 10 hour per day. If work 8 hours then it is 2 hours short; if work 11 hours then there is 1 hour surplus, the last day need to cancel out the collective deviation from the previous 5 days. So we got -2+1-3+2+0=-2 The last day need to have +2 deviation to cancel out the -2 collective deviation to get 10 as average value, so 12.
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