AMC 8 2009 Problem 15

AMC8 2009 年第 15 题

比与比例★★★☆☆

A recipe that makes 5 servings of hot chocolate requires 2 squares of chocolate,

\displaystyle \frac{1}{4}

cup sugar, 1 cup water and 4 cups milk. Jordan has 5 squares of chocolate, 2 cups of sugar, lots of water, and 7 cups of milk. If he maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate he can make?

一种制作 5 份热巧克力的配方需要 2 块巧克力、

\displaystyle \frac{1}{4}

杯糖、1 杯水和 4 杯牛奶。乔丹有 5 块巧克力，2 杯糖，大量的水和 7 杯牛奶。如果她保持相同的配料比例，那么她能做的热巧克力的最大份数是多少？

A. $\displaystyle 5\frac{1}8$
B. $\displaystyle 6\frac{1}4$
C. $\displaystyle 7\frac{1}2$
D. $\displaystyle 8\frac{3}4$
E. $\displaystyle 9\frac{7}8$

正确答案 · Correct Answer

解析 · Solution

Solution 1

Assuming excesses of the other ingredients, the chocolate can make

\frac52 \cdot 5=12.5

servings, the sugar can make

\displaystyle \frac{2}{\frac{1}{4}} \cdot 5 = 40

servings, the water can make unlimited servings, and the milk can make

\frac74 \cdot 5 = 8.75

servings. Limited by the amount of milk, Jordan can make at most

8 \frac34

servings.

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