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, giving her <math>2*\frac{6}{7}</math>.
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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>.
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<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>
 
 
== See also ==
 
== See also ==
* [[2006 AMC 12B Problems/Problem 10 | Previous problem]]
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{{AMC12 box|year=2006|num-b=10|num-a=12|ab=B}}
* [[2006 AMC 12B Problems/Problem 12 | Next problem]]
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* [[2006 AMC 12B Problems]]
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[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 10:45, 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?

$\text {(A) } \frac 67 \qquad \text {(B) } \frac {13}{14} \qquad \text {(C) } 1 \qquad \text {(D) } \frac {14}{13} \qquad \text {(E) } \frac 76$

Solution

Joe has 2 ounces of cream, as stated in the problem.

JoAnn had 14 ounces of liquid, and drank $\frac{1}{7}$ of it. Therefore, she drank $\frac{1}{7}$ of her cream, leaving her $2*\frac{6}{7}$.

$\frac{2}{2*\frac{6}{7}}=\frac{7}{6} \Rightarrow \boxed{\text{(E)}}$

See also

2006 AMC 12B (ProblemsAnswer KeyResources)
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

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