AHSME 1975 Problem 9

Let $a_1, a_2, \ldots$ and $b_1, b_2, \ldots$ be arithmetic progressions such that $a_1 = 25, b_1 = 75$, and $a_{100} + b_{100} = 100$. Find the sum of the first hundred terms of the progression $a_1 + b_1, a_2 + b_2, \ldots$ $\textbf{(A)}\ 0 \textbf{(B)}\ 100 \textbf{(C)}\ 10,000 \textbf{(D)}\ 505,000 \\ \textbf{(E)}\ \text{not enough information given to solve the problem}$