Difference between revisions of "2007 UNCO Math Contest II Problems/Problem 2"
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== Solution == | == Solution == | ||
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| + | Let the number of men be equal to <math>m</math> and the number of women be equal to <math>w</math>, where <math>m</math> and <math>w</math> 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: | ||
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| + | <math>\frac{4}{5}\times m = \frac{3}{7}\times w</math> | ||
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| + | <math>w = \frac{28}{15} m</math> | ||
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| + | Dividing the the number of married persons by the entire adult population gives us: | ||
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| + | <math>Fraction_{married} = \frac{\frac{3}{7}w + \frac{4}{5}m}{m + w}</math> | ||
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| + | <math>Fraction_{married} = \frac{\frac{8}{5}m}{\frac{43}{15}m}</math> | ||
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| + | <math>Fraction_{married} = \frac{24}{43}</math> | ||
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| + | 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: | ||
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| + | <math>Fraction_{married} = \frac{2 \times k m}{m + m \frac{k}{p}}</math> | ||
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| + | <math>Fraction_{married} = \frac{2 p k}{p + k}</math> | ||
== See Also == | == See Also == | ||
Latest revision as of 17:49, 29 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
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 | ||
