1999 AHSME Problems/Problem 8

Problem

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 $1999$?

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

Solution

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 $\boxed{D}$

See Also

1999 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
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