AHSME 1999 Problem 8

At the end of $1994$, Walter was half as old as his grandmother. The sum of the years in which they were born was $3838$. How old will Walter be at the end of $1999$? $\textbf{(A)}\ 48 \textbf{(B)}\ 49 \textbf{(C)}\ 53 \textbf{(D)}\ 55 \textbf{(E)}\ 101$