Difference between revisions of "2006 AMC 12B Problems/Problem 11"
m |
|||
| Line 1: | Line 1: | ||
| − | |||
== 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? | ||
| + | <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 | ||
| + | </math> | ||
| + | == Solution == | ||
| + | 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, giving her <math>2*\frac{6}{7}</math>. |
| − | {{ | + | |
| + | <math>\frac{2}{2*\frac{6}{7}}=\frac{7}{6} \Rightarrow \boxed{\text{(E) }}</math> | ||
== See also == | == See also == | ||
* [[2006 AMC 12B Problems/Problem 10 | Previous problem]] | * [[2006 AMC 12B Problems/Problem 10 | Previous problem]] | ||
* [[2006 AMC 12B Problems/Problem 12 | Next problem]] | * [[2006 AMC 12B Problems/Problem 12 | Next problem]] | ||
* [[2006 AMC 12B Problems]] | * [[2006 AMC 12B Problems]] | ||
Revision as of 13:38, 13 November 2007
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, giving her 
.
