2005 AMC 12B 第 4 题

先试着解答 2005 AMC 12B 第 4 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2005 AMC 12B 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

4.

学年开始时,Lisa 的目标是在全年 5050 次小测中至少 80%80\% 得 A。前 3030 次小测中她有 2222 次得 A。若要达成目标,剩下的小测中她最多有多少次可以低于 A?
At the beginning of the school year, Lisa’s goal was to earn an A on at least 80%80\% of her 5050 quizzes for the year. She earned an A on 2222 of the first 3030 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?
11
22
33
44
55
答案:B
知识点:百分数
小提示:
5050 次小测的 80%80\% 是她需要得 A 的次数。
80%80\% of 5050 quizzes is the number of A’s she needs
大提示:
剩下 2020 次中,她还需要 40−2240 - 22 次 A。
She needs 40−2240 - 22 more A’s out of the remaining 2020 quizzes
解答:
Lisa 至少需要 0.8⋅50=400.8 \cdot 50 = 40 次 A。
她已经有 2222 次,所以剩下 2020 次中还需要 40−22=1840 - 22 = 18 次 A。
因此最多可以有 20−18=220 - 18 = 2 次低于 A。
所以正确答案是 B。
Lisa needs an A on at least 0.8⋅50=400.8 \cdot 50 = 40 quizzes.
She has 2222 already, so she needs 40−22=1840 - 22 = 18 more of the remaining 2020 quizzes.
She can earn a lower grade on at most 20−18=220 - 18 = 2 of them.
Thus, the correct answer is B.
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