# 2013 AMC 12A Problems/Problem 5

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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 1 Simply write down two algebraic equations. We know that Tom gave $t$ dollars and Dorothy gave $d$ dollars. In addition, Tom originally paid $105$ dollars and Dorothy paid $125$ dollars originally. Since they all pay the same amount, we have: $$105 + t = 125 + d.$$ Rearranging, we have $$t-d = \boxed{\textbf{(B)} 20}.$$ Solution $\textcopyright 2018$ RandomPieKevin. All Rights Reserved. skrrt... ## Solution 2 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 $\boxed{\textbf{(B)}}$

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