2009 AMC 8 Problems/Problem 15

Problem

A recipe that makes $5$ servings of hot chocolate requires $2$ squares of chocolate, $\frac{1}{4}$ 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 she maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate she can make?

$\textbf{(A)}\ 5 \frac18 \qquad \textbf{(B)}\ 6\frac14 \qquad \textbf{(C)}\ 7\frac12 \qquad \textbf{(D)}\ 8 \frac34 \qquad \textbf{(E)}\ 9\frac78$

Solution

Asumming excesses of the other ingredients, the chocolate can make $\frac52 \cdot 5=12.5$ servings, the sugar can make $\frac{2}{1/4} \cdot 5 = 40$ 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 $\boxed{\textbf{(D)}\ 8 \frac34}$ servings.

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2009 AMC 8 Problems/Problem 15

Problem

Solution