1999 AHSME Problems/Problem 8

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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 $1999$?

$\textbf{(A)}\ 48 \qquad \textbf{(B)}\  49\qquad \textbf{(C)}\  53\qquad \textbf{(D)}\  55\qquad \textbf{(E)}\ 101$