1991 AMC 12 第 16 题
先试着解答 1991 AMC 12 第 16 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1991 AMC 12 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
16.
去年，世纪高中有一百名学生参加 AHSME，他们的平均分为 。参加 AHSME 的非毕业班学生人数比毕业班学生人数多 ，而毕业班学生的平均分比非毕业班学生高 。毕业班学生的平均分是多少？
One hundred students at Century High School participated in the AHSME last year, and their mean score was The number of non-seniors taking the AHSME was more than the number of seniors, and the mean score of the seniors was higher than that of the non-seniors. What was the mean score of the seniors?
答案：D
小提示：
先求毕业班学生和非毕业班学生的人数
First determine the numbers of seniors and non-seniors
大提示：
设非毕业班学生的平均分为 ，列出加权平均方程
Let the non-senior mean be and form a weighted-average equation
解答：
若有 名毕业班学生，则有 名非毕业班学生，所以 ，从而 。设非毕业班学生的平均分为 ，则毕业班学生的平均分为 。总分方程为 所以 ，毕业班学生的平均分为 。
因此正确答案为 D。
If there are seniors, then there are non-seniors, so and Let the non-senior mean be the senior mean is The total score equation is so and the senior mean is
Thus the correct answer is D.
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