1987 AMC 8 第 16 题

先试着解答 1987 AMC 8 第 16 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 1987 AMC 8 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。

16.

篮球赛季前三场比赛中,乔伊丝前 3030 次投篮命中 1212 次,所以她的赛季投篮命中率是 40%40\%。在下一场比赛中,她投篮 1010 次,并把赛季命中率提高到 50%50\%。这 1010 次投篮中她命中了多少次?
Joyce made 1212 of her first 3030 shots in the first three games of the basketball season, so her seasonal shooting average was 40%.40\%. In her next game, she took 1010 shots and raised her seasonal shooting average to 50%.50\%. How many of these 1010 shots did she make?
22
33
55
66
88
答案:E
知识点:百分数平均数
小提示:
下一场之后,她一共投篮 30+10=4030 + 10 = 40 次
After the next game she has attempted 30+10=4030 + 10 = 40 shots
大提示:
4040 次投篮的 50%50\% 命中率表示总共命中 2020 次;她之前已有 1212 次
A 50%50\% average on 4040 shots means 2020 made in all; she already had 1212
解答:
第四场后她共投篮 4040 次。50%50\% 命中率表示她总共命中 12×40=20\tfrac12 \times 40 = 20 次。
她之前已经命中 1212 次,所以最后 1010 次中命中 20−12=820 - 12 = 8 次。
所以正确答案是 E。
After the fourth game she has taken 4040 shots. A 50%50\% average means she made 12×40=20\tfrac12 \times 40 = 20 shots in total.
She had already made 12,12, so she made 20−12=820 - 12 = 8 of the last 10.10.
Thus, the correct answer is E .
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