# 2006 AMC 10B Problems/Problem 13

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## Problem

Joe and JoAnn each bought $12$ ounces of coffee in a $16$ ounce cup. Joe drank $2$ ounces of his coffee and then added $2$ ounces of cream. JoAnn added $2$ ounces of cream, stirred the coffee well, and then drank $2$ ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee?

$\textbf{(A) } \frac{6}{7}\qquad \textbf{(B) } \frac{13}{14}\qquad \textbf{(C) }1 \qquad \textbf{(D) \ } \frac{14}{13}\qquad \textbf{(E) } \frac{7}{6}$

## Solution

After drinking and adding cream, Joe's cup has $2$ ounces of cream.

After adding cream to her cup, JoAnn's cup had $14$ ounces of liquid. By stirring and then drinking $2$ ounces out of the $14$ ounces of liquid, she drank $\frac{2}{14}=\frac{1}{7}$th of the cream. So there are $2\cdot\frac{6}{7}=\frac{12}{7}$ ounces of cream left.

So the desired ratio is: $2 \div \frac{12}{7}= \boxed{\textbf{(E) }\frac{7}{6}}$.