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Difference between revisions of "2011 AMC 10B Problems/Problem 4"
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LeRoy and Bernardo went on a week-long trip together and agreed to share the costs equally. Over the week, each of them paid for various joint expenses such as gasoline and car rental. At the end of the trip it turned out that LeRoy had paid <math>A</math> dollars and Bernardo had paid <math>B</math> dollars, where <math>A < B</math>. How many dollars must LeRoy give to Bernardo so that they share the costs equally?
 
LeRoy and Bernardo went on a week-long trip together and agreed to share the costs equally. Over the week, each of them paid for various joint expenses such as gasoline and car rental. At the end of the trip it turned out that LeRoy had paid <math>A</math> dollars and Bernardo had paid <math>B</math> dollars, where <math>A < B</math>. How many dollars must LeRoy give to Bernardo so that they share the costs equally?
  
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(A) <math>\frac{A+B}{2}</math>  (B) <math>\frac{A-B}{2}</math> (C) <math>\frac{B-A}{2}</math> (D) <math>B-A</math> (E) <math>A+B</math>
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<math> \textbf{(A)}\ \frac{A + B}{2} \qquad\textbf{(B)}\ \dfrac{A - B}{2}\qquad\textbf{(C)}\ \dfrac{B - A}{2}\qquad\textbf{(D)}\ B - A \qquad\textbf{(E)}\ A + B </math>
  
 
== Solution ==
 
== Solution ==
  
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The difference in how much LeRoy and Bernardo paid is <math>B-A</math>. The average of how much each paid is <math>\frac{A+B}{2}</math>. So LeRoy needs to pay Bernardo <math>\frac{B-A}{2}</math>.
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The difference in how much LeRoy and Bernardo paid is <math>B-A</math>. To share the costs equally, LeRoy must give Bernardo half of the difference, which is <math>\boxed{(C) \frac{B-A}{2}}</math>

Revision as of 19:09, 25 May 2011

Problem

LeRoy and Bernardo went on a week-long trip together and agreed to share the costs equally. Over the week, each of them paid for various joint expenses such as gasoline and car rental. At the end of the trip it turned out that LeRoy had paid $A$ dollars and Bernardo had paid $B$ dollars, where $A < B$. How many dollars must LeRoy give to Bernardo so that they share the costs equally?

$\textbf{(A)}\ \frac{A + B}{2} \qquad\textbf{(B)}\ \dfrac{A - B}{2}\qquad\textbf{(C)}\ \dfrac{B - A}{2}\qquad\textbf{(D)}\ B - A \qquad\textbf{(E)}\ A + B$

Solution

The difference in how much LeRoy and Bernardo paid is $B-A$. To share the costs equally, LeRoy must give Bernardo half of the difference, which is $\boxed{(C) \frac{B-A}{2}}$

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