Difference between revisions of "2006 AMC 10B Problems/Problem 13"
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== Problem == | == Problem == | ||
| + | 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 ammount of cream in Joe's coffee to that in JoAnn's coffee? | ||
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| + | <math> \mathrm{(A) \ } \frac{6}{7}\qquad \mathrm{(B) \ } \frac{13}{14}\qquad \mathrm{(C) \ }1 \qquad \mathrm{(D) \ } \frac{14}{13}\qquad \mathrm{(E) \ } \frac{7}{6} </math> | ||
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== Solution == | == Solution == | ||
| + | After drinking and adding cream, Joe's cup has <math>2</math> ounces of cream. | ||
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| + | After adding cream to her cup, JoAnn's cup had <math>14</math> ounces of liquid. By drinking <math>2</math> ounces out of the <math>14</math> ounces of liquid, she drank | ||
| + | <math>\frac{2}{14}=\frac{1}{7}</math>th of the cream. So there is <math>2\cdot\frac{6}{7}=\frac{12}{7}</math> ounces of cream left. | ||
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| + | So the desired ratio is: <math> \frac{2}{\frac{12}{7}} = \frac{7}{6} \Rightarrow E </math> | ||
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== See Also == | == See Also == | ||
*[[2006 AMC 10B Problems]] | *[[2006 AMC 10B Problems]] | ||
Revision as of 22:35, 13 July 2006
Problem
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 ammount of cream in Joe's coffee to that in JoAnn's coffee?
Solution
After drinking and adding cream, Joe's cup has 
ounces of cream.
After adding cream to her cup, JoAnn's cup had 
ounces of liquid. By drinking ounces out of the ounces of liquid, she drank
th of the cream. So there is 
ounces of cream left.
So the desired ratio is: 
