Difference between revisions of "2007 UNCO Math Contest II Problems/Problem 2"
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| − | <math> | + | <math>Fraction_{married} = \frac{\frac{3}{7}w + \frac{4}{5}m}{m + w}</math> |
| − | <math> | + | <math>Fraction_{married} = \frac{\frac{8}{5}m}{\frac{43}{15}m}</math> |
| − | <math> | + | <math>Fraction_{married} = \frac{24}{43}</math> |
| + | |||
| + | Using the above statements, we can derive a generalized formula. If <math>k</math> is the fraction of married men and <math>p</math> is the fraction of married women, then: | ||
| + | |||
| + | <math>Fraction_{married} = \frac{2 \times k m}{m + m \frac{k}{p}}</math> | ||
| + | |||
| + | <math>Fraction_{married} = \frac{2 p k}{p + k}</math> | ||
== See Also == | == See Also == | ||
Revision as of 19:22, 28 January 2018
Problem
In Grants Pass, Oregon 
of the men are married to 
of the women.
What fraction of the adult population is married? Give a possible generalization.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Let the number of men be equal to 
and the number of women be equal to 
, where and are positive whole numbers. Assuming a marriage consists of one man and one woman, we see that the number of married men is equal to the number of married women in the equation:
Dividing the the number of married persons by the entire adult population gives us:
Using the above statements, we can derive a generalized formula. If 
is the fraction of married men and 
is the fraction of married women, then:
See Also
| 2007 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
