Proportions of Men to WomenDate: 4/18/96 at 8:44:43 From: Steve Higgins Subject: Fractions and proportions Dear Dr Math I have a maths puzzle I hope you can help me with.... "In a certain village 2/3 (two thirds) of the men are married to 3/5 (three fifths) of the women. What proportion of the population as a whole is married?" I assume a traditional marriage arrangement exists of one male to one female and that no one is married to anyone living outside of the village...... Not a very PC problem but I can't remember how to do the math anyway. I hope you can help..... Steve Higgins Date: 4/24/96 at 12:20:16 From: Doctor Cameron Subject: Re: Fractions and proportions Thanks for writing in. First, assign variables. x = male population y = female population z = percentage of married people Assuming that every one married male is married to one female: 2/3 x = 3/5 y divide both sides by 2/3 x = 9/10 y So the male population is nine-tenths the size of the female population. z = the percentage of married people that is married/total population z = (2/3 x + 3/5 y)/(x+y) But we substitute for x: z = (2/3 (9/10 y) + 3/5 y)/(9/10 y +y) We do some calculations: z = (3/5 y + 3/5 y)/(19/10 y)... This just makes sense because the number of married people should be 2* 3/5 y. z = 6/5 y/(19/10)y Divide out the y's: z = (6/5)/(19/10) or z= 12/19 If we divide that out we see that 63.1% of the population is married. -Doctor Cameron, The Math Forum |
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