2019 AMC 8 第 7 题

先试着解答 2019 AMC 8 第 7 题,然后核对你的答案与视频与精心整理的解答,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 2019 AMC 8 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。

7.

Shauna 参加五次测试,每次满分 100100 分。她前三次成绩是 7676、9494 和 8787。为了五次测试平均分达到 8181,另外两次测试中她可能得到的最低分是多少?
Shauna takes five tests, each worth a maximum of 100100 points. Her scores on the first three tests are 76,76, 94,94, and 87.87. In order to average 8181 for all five tests, what is the lowest score she could earn on one of the other two tests?
4848
5252
6666
7070
7474
答案:A
知识点:平均数最优化
小提示:
五次成绩总和必须是 5⋅815\cdot81
The five scores must total 5⋅815\cdot81
大提示:
让剩下两次中的一次尽可能高
Make one remaining score as large as possible
视频讲解:
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文字解答:
要让其中一次成绩尽可能低,就让另一次成绩尽可能高。假设 Shauna 第四次测试得 100100 分。
这 44 次测试的总分为 76+94+87+100=357。 76 + 94 + 87 + 100 = 357\text{。}若五次平均分为 8181,总分必须为 5⋅81=4055 \cdot 81 = 405,所以最后一次需要 405−357=48405 - 357 = 48 分。
正确答案是 A。
To minimize one of the scores, we have to maximize the other score. Assume that Shauna gets a 100100 on her fourth test.
The sum of the 44 tests is then 76+94+87+100=357. 76 + 94 + 87 + 100 = 357. For an average of 81,81, Shauna’s test scores must add to 5⋅81=405.5 \cdot 81 = 405. This means that she needs to get a 405−357=48405 - 357 = 48 on her last test.
Thus, the correct answer is A.
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