Difference between revisions of "2006 AMC 12B Problems/Problem 11"
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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 amount of cream in Joe's coffee to that in JoAnn's coffee? | 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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<math> | <math> | ||
\text {(A) } \frac 67 \qquad \text {(B) } \frac {13}{14} \qquad \text {(C) } 1 \qquad \text {(D) } \frac {14}{13} \qquad \text {(E) } \frac 76 | \text {(A) } \frac 67 \qquad \text {(B) } \frac {13}{14} \qquad \text {(C) } 1 \qquad \text {(D) } \frac {14}{13} \qquad \text {(E) } \frac 76 | ||
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Joe has 2 ounces of cream, as stated in the problem. | Joe has 2 ounces of cream, as stated in the problem. | ||
| − | JoAnn had 14 ounces of liquid, and drank <math>\frac{1}{7}</math> of it. Therefore, she drank <math>\frac{1}{7}</math> of her cream, | + | JoAnn had 14 ounces of liquid, and drank <math>\frac{1}{7}</math> of it. Therefore, she drank <math>\frac{1}{7}</math> of her cream, leaving her <math>2*\frac{6}{7}</math>. |
<math>\frac{2}{2*\frac{6}{7}}=\frac{7}{6} \Rightarrow \boxed{\text{(E)}}</math> | <math>\frac{2}{2*\frac{6}{7}}=\frac{7}{6} \Rightarrow \boxed{\text{(E)}}</math> | ||
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== See also == | == See also == | ||
{{AMC12 box|year=2006|num-b=10|num-a=12|ab=B}} | {{AMC12 box|year=2006|num-b=10|num-a=12|ab=B}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 09:45, 4 July 2013
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 amount of cream in Joe's coffee to that in JoAnn's coffee?
Solution
Joe has 2 ounces of cream, as stated in the problem.
JoAnn had 14 ounces of liquid, and drank 
of it. Therefore, she drank of her cream, leaving her 
.
See also
| 2006 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 10 |
Followed by Problem 12 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
