Ratio of Ratios
Date: 06/05/2002 at 22:14:17 From: Tereasa Holland Subject: WORD PROBLEM A particular condominium complex is an adults-only complex. In this complex, 3/5 of the men are married to 2/3 of the women. What fraction of the residents are married? Explain the solution.
Date: 06/06/2002 at 15:03:11 From: Doctor Ian Subject: Re: WORD PROBLEM Hi Tereasa, Suppose there are 5 men. Then we have this situation: married m m m unmarried m m We have to have at least 3 women, to be married to the men... but 3 isn't 2/3 of any integer. So we have to have at least 6 women: married m m m w w w w w w unmarried m m w w w Which means we need at least 3 more men: married m m m m m m w w w w w w unmarried m m m m w w w The entire population has to be some multiple of this population, right? We could have arrived here more quickly by noting that if m is the number of men, and w is the number of women, then the numbers of married men and women have to be equal (unless you want to start considering gay marriage, polygamy, and other alternative arrangements... in which case there is no way to answer the question), so 3 2 - m = - w 5 3 3*3 m = 2*5 w Cross multiply 9m = 10w So there has to be a ratio of 9 men to 10 women, which is what our picture shows. Can you take it from here? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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