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 $2$ ounces of cream and drinks nothing afterward, so he has $2$ ounces of cream.

JoAnn has $12$ ounces of coffee plus $2$ ounces of cream, making $14$ ounces of uniform mixture. After drinking $2$ ounces she keeps $\tfrac{12}{14}=\tfrac67$ of her cream, which is $\tfrac67\cdot2=\tfrac{12}{7}$ ounces.

The ratio is $2\div\tfrac{12}{7}=\tfrac{7}{6}.$

Thus, the correct answer is E.

2006 AMC 10B Problem 13

Solution:

Problem 13 in Other Years