1999 AMC 8 第 17 题

先试着解答 1999 AMC 8 第 17 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。

17.

第 1717、1818 和 1919 题参考以下内容:
给一群人做饼干
中央中学有 108108 名参加 AMC 88 的学生,他们晚上聚在一起讨论题目,并且平均每人吃两个饼干。今年沃尔特和格蕾特要烤邦妮牌美味条形饼干。这个食谱每盘做 1515 个饼干,配料包括:1121\dfrac{1}{2} 杯面粉、22 个鸡蛋、33 汤匙黄油、34\dfrac{3}{4} 杯糖和 11 包巧克力粒。他们只做完整份食谱,不做部分份。
沃尔特可以按半打购买鸡蛋。为了做足够的饼干,他应该买多少半打鸡蛋?(可能会剩下一些鸡蛋和一些饼干。)
Problems 17,17, 18,18, and 1919 refer to the following:
Cookies For a Crowd
At Central Middle School the 108108 students who take the AMC 88 meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie’s Best Bar Cookies this year. Their recipe, which makes a pan of 1515 cookies, lists these items: 1121\dfrac{1}{2} cups of flour, 22 eggs, 33 tablespoons butter, 34\dfrac{3}{4} cups sugar, and 11 package of chocolate drops. They will make only full recipes, not partial recipes.
Walter can buy eggs by the half-dozen. How many half-dozens should he buy to make enough cookies? (Some eggs and some cookies may be left over.)
11
22
55
77
1515
答案:C
知识点:取整函数单位换算
小提示:
先求做 216216 个饼干需要多少完整份食谱
Find how many full recipes are needed for 216216 cookies
大提示:
每份完整食谱用 22 个鸡蛋
Each full recipe uses 22 eggs
解答:
因为学生平均每人吃 22 个饼干,他们总共会吃 108⋅2=216108 \cdot 2 = 216 个饼干。
每份食谱做 1515 个饼干,所以需要 ⌈21615⌉=15 \left\lceil\dfrac{216}{15}\right\rceil = 15 份完整食谱,才能做够。
每盘需要 22 个鸡蛋,所以需要 15⋅2=3015 \cdot 2 = 30 个鸡蛋。半打是 66 个鸡蛋,因此需要 30÷6=530 \div 6 = 5 个半打。
所以正确答案是 C。
Since the students eat an average of 22 cookies each, they will eat a total of 108⋅2=216108 \cdot 2 = 216 cookies.
Each recipe makes 1515 cookies, which means we need ⌈21615⌉=15 \left\lceil\dfrac{216}{15}\right\rceil = 15 full recipes to make enough cookies.
Each pan requires 22 eggs, which means we need 15⋅2=3015 \cdot 2 = 30 eggs. There are 66 eggs in a half-dozen, so we need 30÷6=530 \div 6 = 5 half-dozens.
Thus, C is the correct answer.
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