2013 AMC 12A Problems/Problem 5

Revision as of 15:56, 3 July 2013 by Kj2002 (talk | contribs) (See also)

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 the 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

Add up the amounts that Tom, Dorothy, and Sammy paid to get $$405$, and divide by 3 to get $$135$, the amount that each should have paid.

Tom, having paid $$105$, owes Sammy $$30$, and Dorothy, having paid $$125$, owes Sammy $$10$.

Thus, $t - d = 30 - 10 = 20$, which is $\boxed{\textbf{(B)}}$

See also

2013 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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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