Question

Shauna 参加五次测试，每次满分 $100$ 分。她前三次成绩是 $76$ 、 $94$ 和 $87$ 。为了五次测试平均分达到 $81$ ，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 $100$ points. Her scores on the first three tests are $76,$ $94,$ and $87.$ In order to average $81$ for all five tests, what is the lowest score she could earn on one of the other two tests?

$48$

$52$

$66$

$70$

$74$

答案：A

知识点：平均数最优化

难度评级：960

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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 $100$ 分。

这 $4$ 次测试的总分为若五次平均为 $81$ ，总分必须为 $5 \cdot 81 = 405$ ，所以最后一次需要 $405 - 357 = 48$ 分。 $76 + 94 + 87 + 100 = 357.$

正确答案是 A。

To minimize one of the scores, we have to maximize the other score. Assume that Shauna gets a $100$ on her fourth test.

The sum of the $4$ tests is then $76 + 94 + 87 + 100 = 357.$ For an average of $81,$ Shauna's test scores must add to $5 \cdot 81 = 405.$ This means that she needs to get a $405 - 357 = 48$ on her last test.

Thus, the correct answer is A.

2019 AMC 8 第 7 题

答案：A

难度评级：960

视频讲解：

文字解答：

其他年份的第 7 题