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 $1999$?
$\textbf{(A)}\ 48 \qquad \textbf{(B)}\  49\qquad \textbf{(C)}\  53\qquad \textbf{(D)}\  55\qquad \textbf{(E)}\ 101$
In $1994$, if Water is $x$ years old, then Walter's grandmother is $2x$ years old.
This means that Walter was born in $1994 - x$, and Walter's grandmother was born in $1994 - 2x$.
The sum of those years is $3838$, so we have:
$1994 - x + 1994 - 2x = 3838$
$3988 - 3x = 3838$
$x = 50$
If Walter is $50$ years old in $1994$, then he will be $55$ years old in $1999$, thus giving answer $\boxed{D}$