1999 AMC 12 Problem 8

Attempt Problem 8 of the 1999 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1999 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

At the end of $1994$ Walter was half as old as his grandmother. The sum of the years in which they were born is $3838.$ How old will Walter be at the end of $1999?$

$48$

$49$

$53$

$55$

$101$

Answer: D

Concepts:ages linear equation

Difficulty rating: 1240

Solution:

Let Walter be $w$ years old at the end of $1994,$ so his grandmother is $2w.$ Their birth years are $1994 - w$ and $1994 - 2w,$ and $\begin{aligned} &(1994 - w) \\ &\quad {}+ (1994 - 2w) = 3838. \end{aligned}$ This gives $3988 - 3w = 3838,$ so $w = 50.$

At the end of $1999,$ Walter will be $50 + 5 = 55.$

Thus, the correct answer is D.

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