Difference between revisions of "2004 AMC 8 Problems/Problem 22"
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==Problem== | ==Problem== | ||
| − | At a party there are only single women and married men with their wives. The probability that a randomly selected woman is single is <math>\frac25</math>. What fraction of the people in the room are married men | + | At a party there are only single women and married men with their wives. The probability that a randomly selected woman is single is <math>\frac25</math>. What fraction of the people in the room are married men? |
<math>\textbf{(A)}\ \frac13\qquad \textbf{(B)}\ \frac38\qquad \textbf{(C)}\ \frac25\qquad \textbf{(D)}\ \frac{5}{12}\qquad \textbf{(E)}\ \frac35</math> | <math>\textbf{(A)}\ \frac13\qquad \textbf{(B)}\ \frac38\qquad \textbf{(C)}\ \frac25\qquad \textbf{(D)}\ \frac{5}{12}\qquad \textbf{(E)}\ \frac35</math> | ||
| − | + | ||
==Solution== | ==Solution== | ||
| − | Assume arbitrarily there are <math>5</math> women in the room, of which <math>5 \cdot \frac25 = 2</math> are single and <math>5-2=3</math> are married. Each married woman came with her husband, so there are <math>3</math> married men in the room as well for a total of <math>5+3=8</math> people. The fraction of the people that are married men is <math>\boxed{\textbf{(B)}\ \frac38}</math>. | + | Assume arbitrarily (and WLOG) there are <math>5</math> women in the room, of which <math>5 \cdot \frac25 = 2</math> are single and <math>5-2=3</math> are married. Each married woman came with her husband, so there are <math>3</math> married men in the room as well for a total of <math>5+3=8</math> people. The fraction of the people that are married men is <math>\boxed{\textbf{(B)}\ \frac38}</math>. |
==See Also== | ==See Also== | ||
{{AMC8 box|year=2004|num-b=21|num-a=23}} | {{AMC8 box|year=2004|num-b=21|num-a=23}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 22:43, 27 September 2017
Problem
At a party there are only single women and married men with their wives. The probability that a randomly selected woman is single is 
. What fraction of the people in the room are married men?
Solution
Assume arbitrarily (and WLOG) there are 
women in the room, of which 
are single and 
are married. Each married woman came with her husband, so there are 
married men in the room as well for a total of 
people. The fraction of the people that are married men is 
.
See Also
| 2004 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 21 |
Followed by Problem 23 | |
| 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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
