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Difference between revisions of "2009 AMC 8 Problems/Problem 15"
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Asumming excesses of the other ingredients, the chocolate can make <math>\frac52 \cdot 5=12.5</math> servings, the sugar can make <math>\frac{2}{1/4} \cdot 5 = 40</math> servings, the water can make unlimited servings, and the milk can make <math>\frac74 \cdot 5 = 8.75</math> servings. The Limited by the amount of milk, Jordan can make at most <math>\boxed{\textbf{(D)}\ 8 \frac34}</math> servings.
 
Asumming excesses of the other ingredients, the chocolate can make <math>\frac52 \cdot 5=12.5</math> servings, the sugar can make <math>\frac{2}{1/4} \cdot 5 = 40</math> servings, the water can make unlimited servings, and the milk can make <math>\frac74 \cdot 5 = 8.75</math> servings. The Limited by the amount of milk, Jordan can make at most <math>\boxed{\textbf{(D)}\ 8 \frac34}</math> servings.
  
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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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{{AMC8 box|year=2009|num-b=14|num-a=16}}
 
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{{MAA Notice}}
 

Revision as of 12:54, 23 July 2013

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. The Limited by the amount of milk, Jordan can make at most $\boxed{\textbf{(D)}\ 8 \frac34}$ servings.

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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