AMC10 2005 B

AMC10 2005 B · Q6

AMC10 2005 B · Q6. It mainly tests Percent, Averages (mean).

At the beginning of the school year, Lisa's goal was to earn an A on at least 80% of her 50 quizzes for the year. She earned an A on 22 of the first 30 quizzes. If she is to achieve her goal, on at most how many of the remaining quizzes can she earn a grade lower than an A?

在学年初，Lisa的目标是在全年50次小测验中至少获得80%的A。她在前30次小测验中获得了22次A。如果她要实现目标，在剩余的小测验中最多能有多少次获得低于A的成绩？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (B)

正确答案：（B）

Solution

To earn an A on at least 80% of her quizzes, Lisa needs to receive an A on at least $(0.8)(50) = 40$ quizzes. Thus she must earn an A on at least $40 - 22 = 18$ of the remaining 20. So she can earn a grade lower than an A on at most 2 of the remaining quizzes.

要获得至少80%的A，Lisa需要至少获得$(0.8)(50) = 40$次A。因此，她必须在剩余20次中至少获得$40 - 22 = 18$次A。所以，她最多能在剩余小测验中获得2次低于A的成绩。

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