2006 AMC 12B Problem 11

Problem 11 of 25IntermediateAlgebra

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?

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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}{\,\frac{12}{7}\,} = \frac{14}{12} = \frac{7}{6}.

Thus, the correct answer is E.