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

Let Walter be

w

and his grandmother

2w

at the end of

1994

Their birth years are

1994 - w

and

1994 - 2w

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,

w = 50.

At the end of

1999,

Walter will be

50 + 5 = 55.

Thus, the correct answer is D.

Problem 8 in other years