Question

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?

$\dfrac{6}{7}$

$\dfrac{13}{14}$

$1$

$\dfrac{14}{13}$

$\dfrac{7}{6}$

Solution:

Joe adds the cream last, so his cup holds all $2$ ounces of cream.

JoAnn's cup has $14$ ounces of mixture containing $2$ ounces of cream. Drinking $2$ ounces removes a fraction $\tfrac{2}{14}$ of everything, leaving $2 \cdot \frac{12}{14} = \frac{12}{7}$ ounces of cream.

The ratio is $\frac{2}{\,12/7\,} = \frac{14}{12} = \frac{7}{6}.$

Thus, the correct answer is E.

2006 AMC 12B Problem 11

Solution:

Problem 11 in Other Years