1999 AMC 8 第 19 题

先试着解答 1999 AMC 8 第 19 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 1999 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。

19.

鼓手生病了,音乐会取消了。沃尔特和格蕾特必须烤出足够的饼干,共计 216216 块。每条黄油相当于 88 汤匙。需要多少条黄油?(当然,可能会剩下一些黄油。)
The drummer gets sick. The concert is cancelled. Walter and Gretel must make enough pans of cookies to supply 216216 cookies. There are 88 tablespoons in a stick of butter. How many sticks of butter will be needed? (Some butter may be left over, of course.)
55
66
77
88
99
答案:B
知识点:单位换算取整函数
小提示:
先把需要的盘数向上取整
First round the number of pans up
大提示:
将黄油汤匙数换算成条数并向上取整
Convert tablespoons of butter to sticks and round up
解答:
要做 216216 个饼干,他们必须做 ⌈21615⌉=15 \left\lceil \dfrac{216}{15} \right\rceil = 15 盘。每盘需要 33 汤匙黄油,所以所有饼干共需要 15⋅3=4515 \cdot 3 = 45 汤匙。
因此他们需要 ⌈458⌉=6 \left\lceil \dfrac{45}{8} \right\rceil = 6 条黄油。
所以正确答案是 B。
To make 216216 cookies, they have to make ⌈21615⌉=15 \left\lceil \dfrac{216}{15} \right\rceil = 15 pans. Since each pan requires 33 tablespoons of butter, all the pans will need 15⋅3=4515 \cdot 3 = 45 tablespoons.
They will then need ⌈458⌉=6 \left\lceil \dfrac{45}{8} \right\rceil = 6 sticks of butter.
Thus, B is the correct answer.
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