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Difference between revisions of "1999 AHSME Problems/Problem 8"

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==Problem==
 
==Problem==
  
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==Solution==
 
==Solution==
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In <math>1994</math>, if Water is <math>x</math> years old, then Walter's grandmother is <math>2x</math> years old.
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This means that Walter was born in <math>1994 - x</math>, and Walter's grandmother was born in <math>1994 - 2x</math>.
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The sum of those years is <math>3838</math>, so we have:
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<math>1994 - x + 1994 - 2x = 3838</math>
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<math>3988 - 3x = 3838</math>
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<math>x = 50</math>
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If Walter is <math>50</math> years old in <math>1994</math>, then he will be <math>55</math> years old in <math>1999</math>, thus giving answer <math>\boxed{D}</math>
  
 
==See Also==
 
==See Also==
  
 
{{AHSME box|year=1999|num-b=7|num-a=9}}
 
{{AHSME box|year=1999|num-b=7|num-a=9}}
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{{MAA Notice}}

Latest revision as of 13:34, 5 July 2013

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 (Problems • Answer Key • Resources)
Preceded by
Problem 7 		Followed by
Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

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