Difference between revisions of "1999 AHSME Problems/Problem 8"
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| + | ==Problem== | ||
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At the end of <math> 1994</math>, Walter was half as old as his grandmother. The sum of the years in which they were born was <math> 3838</math>. How old will Walter be at the end of <math> 1999</math>? | At the end of <math> 1994</math>, Walter was half as old as his grandmother. The sum of the years in which they were born was <math> 3838</math>. How old will Walter be at the end of <math> 1999</math>? | ||
<math> \textbf{(A)}\ 48 \qquad \textbf{(B)}\ 49\qquad \textbf{(C)}\ 53\qquad \textbf{(D)}\ 55\qquad \textbf{(E)}\ 101</math> | <math> \textbf{(A)}\ 48 \qquad \textbf{(B)}\ 49\qquad \textbf{(C)}\ 53\qquad \textbf{(D)}\ 55\qquad \textbf{(E)}\ 101</math> | ||
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| + | ==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> | ||
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| + | ==See Also== | ||
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| + | {{AHSME box|year=1999|num-b=7|num-a=9}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 13:34, 5 July 2013
Problem
At the end of 
, Walter was half as old as his grandmother. The sum of the years in which they were born was 
. How old will Walter be at the end of 
?
Solution
In , if Water is 
years old, then Walter's grandmother is 
years old.
This means that Walter was born in 
, and Walter's grandmother was born in 
.
The sum of those years is , so we have:
If Walter is 
years old in , then he will be 
years old in , thus giving answer 
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
