Proportions of Men to Women

Date: 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