AMC 12 2015b Problem 12

Let $a$, $b$, and $c$ be three distinct one-digit numbers. What is the maximum value of the sum of the roots of the equation $(x-a)(x-b)+(x-b)(x-c)=0$ ?

\textbf{(A)} 15 \textbf{(B)} 15.5 \textbf{(C)} 16 \textbf{(D)} 16.5 \textbf{(E)} 17