2006 AMC 10B Problem 13

Problem 13 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

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.