# 2013 AMC 12A Problems/Problem 5

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 $\boxed{\textbf{(B)}}$