AMC8 2012

AMC8 2012 · Q7

AMC8 2012 · Q7. It mainly tests Linear equations, Averages (mean).

Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of at least 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?

伊莎贝拉在数学课上必须参加四次满分100分的测试。她的目标是测试平均分至少95分。她前两次测试分数分别是97和91。在看到第三次测试分数后，她意识到自己仍然能达到目标。她第三次测试的最低可能分数是多少？

(A) 90 90

(B) 92 92

(D) 96 96

(E) 97 97

Answer

Correct choice: (B)

正确答案：（B）

Solution

Isabella wants an average grade of $95$ on her 4 tests; this also means that she wants the sum of her test scores to be at least $95 \times 4 = 380$ (if she goes over this number, she'll be over her goal!). She's already taken two tests, which sum to $97+91 = 188$, which means she needs $192$ more points to achieve her desired average. In order to minimize the score on the third test, we assume that Isabella will receive all $100$ points on the fourth test. Therefore, the lowest Isabella could have scored on the third test would be $192-100 = \boxed{\textbf{(B)}\ 92}$.

伊莎贝拉希望四次测试平均分达到$95$，这意味着总分至少$95 \times 4 = 380$（如果超过这个数，她就超过目标了！）。她已经考了两次，总分$97+91 = 188$，因此她还需要$192$分来达到期望平均分。为了最小化第三次测试分数，我们假设她第四次测试得到满分$100$分。因此，第三次测试的最低分数是$192-100 = \boxed{\textbf{(B)}\ 92}$。

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