Question

Isabella 的数学课必须参加四次满分一百分的测试。她的目标是四次测试平均分达到九十五。她前两次测试成绩是九十七和九十一。看到第三次测试成绩后，她意识到自己仍然可以达到目标。她第三次测试最低可能得多少分？

Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of 95 on the tests. Her first two test scores were 97 and 91. After seeing her score on the third test, she realized that she could still reach her goal. What is the lowest possible score she could have made on the third test?

$90$

$92$

$95$

$96$

$97$

答案：B

知识点：平均数最优化

难度评级：1070

视频讲解：

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文字解答：

若平均分为 $95$ ，四次测试总分为 $95\cdot 4 = 380$ 。由于已知前两次成绩，后两次测试总分是 $380$ 减去前两次成绩。

后两次测试总分必须为 $380-91-97 = 192$ 。因此后两次成绩之和为 $192$ 。

要使第三次成绩最低，就让第四次成绩最高，为 $100$ 。于是第三次成绩为 $192 -100 = 92$ 。

所以正确答案是 B。

If the average is $95,$ then the sum of the tests is $95\cdot 4 = 380 .$ Since we have the first two tests, the sum of the last two tests is $380$ minus the first two scores.

This makes the sum of the last two scores equal to $380-91-97 = 192.$ Her last two scores therefore have a sum of $192.$

Given the sum of the tests we try to minimize one score, then we must maximize the other test. Therefore, we maximize the fourth test by making it $100.$ This would make the third test equal to $192 -100 = 92.$

Thus, the answer is B .

2012 AMC 8 第 7 题

答案：B

难度评级：1070

视频讲解：

文字解答：

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