Difference between revisions of "2013 AMC 10A Problems/Problem 5"

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==Problem==
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Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly.  During their trip Tom paid &#036;105, Dorothy paid &#036;125, and Sammy paid &#036;175.  In order to share costs equally, Tom gave Sammy <math>t</math> dollars, and Dorothy gave Sammy <math>d</math> dollars.  What is <math>t-d</math>?
 
Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly.  During their trip Tom paid &#036;105, Dorothy paid &#036;125, and Sammy paid &#036;175.  In order to share costs equally, Tom gave Sammy <math>t</math> dollars, and Dorothy gave Sammy <math>d</math> dollars.  What is <math>t-d</math>?
  
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<math> \textbf{(A)}\ 15\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 25\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 35 </math>
 
<math> \textbf{(A)}\ 15\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 25\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 35 </math>
  
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==Solution==
  
 
The total amount paid is <math>105 + 125 + 175 = 405</math>.  To get how much each should have paid, we do <math>405/3 = 135</math>
 
The total amount paid is <math>105 + 125 + 175 = 405</math>.  To get how much each should have paid, we do <math>405/3 = 135</math>
  
 
Thus, we know that Tom needs to give Sammy 30 dollars, and Dorothy 10 dollars.  This means that <math>t-d = 30 - 10 = 20</math>, <math>\textbf{(B)}</math>
 
Thus, we know that Tom needs to give Sammy 30 dollars, and Dorothy 10 dollars.  This means that <math>t-d = 30 - 10 = 20</math>, <math>\textbf{(B)}</math>

Revision as of 18:22, 7 February 2013

Problem

Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly. During their trip Tom paid $105, Dorothy paid $125, and Sammy paid $175. In order to share costs equally, Tom gave Sammy $t$ dollars, and Dorothy gave Sammy $d$ dollars. What is $t-d$?


$\textbf{(A)}\ 15\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 25\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 35$

Solution

The total amount paid is $105 + 125 + 175 = 405$. To get how much each should have paid, we do $405/3 = 135$

Thus, we know that Tom needs to give Sammy 30 dollars, and Dorothy 10 dollars. This means that $t-d = 30 - 10 = 20$, $\textbf{(B)}$