2009 AMC 8 第 15 题

先试着解答 2009 AMC 8 第 15 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 2009 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。

15.

一份可做 55 份热巧克力的食谱需要 22 块巧克力、14\dfrac{1}{4} 杯糖、11 杯水和 44 杯牛奶。乔丹有 55 块巧克力、22 杯糖、很多水和 77 杯牛奶。如果她保持相同的配料比例,最多能做多少份热巧克力?
A recipe that makes 55 servings of hot chocolate requires 22 squares of chocolate, 14\dfrac{1}{4} cup sugar, 11 cup water and 44 cups milk. Jordan has 55 squares of chocolate, 22 cups of sugar, lots of water, and 77 cups of milk. If she maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate she can make?
5185 \dfrac{1}{8}
6146 \dfrac{1}{4}
7127 \dfrac{1}{2}
8348 \dfrac{3}{4}
9789 \dfrac{7}{8}
答案:D
知识点:比与比例
小提示:
比较每种配料分别能支持多少批食谱
Compare how many recipe batches each ingredient can support.
大提示:
能支持批数最少的配料限制了份数
The ingredient that supports the fewest batches limits the servings.
解答:
需要找出哪种配料是限制因素。
乔丹的巧克力足够做 5÷2=525\div2=\dfrac{5}{2} 批,糖足够做 2÷14=82\div\dfrac{1}{4}=8 批,牛奶足够做 7÷4=747\div4=\dfrac{7}{4} 批。
牛奶是限制因素,所以乔丹可以做 5⋅74=354=8345\cdot\dfrac{7}{4}=\dfrac{35}{4}=8\dfrac{3}{4} 份。
所以正确答案是 D。
We need to find which ingredient is the limiting factor.
Jordan has enough chocolate for 5÷2=525\div2=\dfrac{5}{2} batches, enough sugar for 2÷14=82\div\dfrac{1}{4}=8 batches, and enough milk for 7÷4=747\div4=\dfrac{7}{4} batches.
The milk is limiting, so Jordan can make 5⋅74=354=8345\cdot\dfrac{7}{4}=\dfrac{35}{4}=8\dfrac{3}{4} servings.
Thus, D is the correct answer.
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