# 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 .