AMC12 2006 12B, Problem 11

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?

Solution: Joe has 2 ounces of cream, as stated in the problem. JoAnn had 14 ounces of liquid, and drank $\frac{1}{7}$ of it. Therefore, she drank $\frac{1}{7}$ of her cream, leaving her $2*\frac{6}{7}$. $\frac{2}{2*\frac{6}{7}}=\frac{7}{6} \Rightarrow \fbox{\frac 76}$

Answer: \frac 76