2013 AMC 12A Problems/Problem 5
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[hide]Problem
Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly. During their trip Tom paid $, Dorothy paid $, and Sammy paid $. In order to share the costs equally, Tom gave Sammy dollars, and Dorothy gave Sammy dollars. What is ?
Solution 1
Simply write down two algebraic equations. We know that Tom gave dollars and Dorothy gave dollars. In addition, Tom originally paid dollars and Dorothy paid dollars originally. Since they all pay the same amount, we have: Rearranging, we have
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Solution 2
Add up the amounts that Tom, Dorothy, and Sammy paid to get $, and divide by 3 to get $, the amount that each should have paid.
Tom, having paid $, owes Sammy $, and Dorothy, having paid $, owes Sammy $.
Thus, , which is
See also
2013 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 4 |
Followed by Problem 6 |
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All AMC 12 Problems and Solutions |
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