AMC 8 2012 Problem 7
AMC8 2012 年第 7 题
方程与不等式★★☆☆☆
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 she can still reach her goal. What is the lowest possible score she could have made on the third test?
Isabella 必须参加 4 场满分都是 100 分的数学考试。她的目标是平均分达到 95 分。她的前 2 场考试的分数是 97 分和 91 分。当她看到第三场考试分数后，她意识到她还是可以达到她的目标的。那么第三场考试她可能考到的最低分数是多少？
- A.
- B.
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- D.
- E.
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
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 95×4 = 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 = 92.
Isabella needs to lose a max of 20. When she got 97 and 91, the max goes down to 20 - 3 - 9 = 8. If we get 100 on her last test, then she will get 92 on the third test.
Let the sum of the first three test scores be . If it's still possible to get an average of 95 after the third test, then the lowest score possible would be Then, solving the equation, we get x = 280. Given that the previous test scores are 97 and 91, we can subtract those score from it, which would give that the lowest score possible for the test is 280 - 97 - 91 = 92
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