2013 AMC 10A Problems/Problem 5: Difference between revisions
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==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 <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 $105, Dorothy paid $125, and Sammy paid $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> | ||
==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 
dollars, and Dorothy gave Sammy 
dollars. What is 
?
Solution
The total amount paid is 
. To get how much each should have paid, we do 
Thus, we know that Tom needs to give Sammy 30 dollars, and Dorothy 10 dollars. This means that 
, 
