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==Puzzle== | ==Puzzle== | ||
In a certain condominium community, 2/3 of all the women are married and 3/5 of all the men are married. What fraction of the entire condominium community is married? | In a certain condominium community, 2/3 of all the women are married (to men) and 3/5 of all the men are married (to women). What fraction of the entire condominium community is married? | ||
{{Solution| The fraction of married women (M) to unmarried women (U) and the fraction of married men (M) to unmarried men (U) can be visualized as follows. | {{Solution| The fraction of married women (M) to unmarried women (U) and the fraction of married men (M) to unmarried men (U) can be visualized as follows. | ||
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We know that the number of women who are married equals the number of men who are married. So the women’s M region and the men’s M region must be the same size. By using the same units in both the women’s diagram and the men’s diagram, we see that the two M regions are six units long each. This represents a total of 12 units out of a total possible of 19 units (9 from the women plus 10 from the men). So 12/19 of the condominium community is married.}} | We know that the number of women who are married equals the number of men who are married. So the women’s M region and the men’s M region must be the same size. By using the same units in both the women’s diagram and the men’s diagram, we see that the two M regions are six units long each. This represents a total of 12 units out of a total possible of 19 units (9 from the women plus 10 from the men). So 12/19 of the condominium community is married.}} | ||
[[Category: Algebra]] | |||
Current revision as of 19:15, 4 April 2015
Puzzle
In a certain condominium community, 2/3 of all the women are married (to men) and 3/5 of all the men are married (to women). What fraction of the entire condominium community is married?
Solution