Problem: In a town, two thirds of the males are married, and three fifths of the females are married. (Marriage between a man and woman) What fraction of the people (male and female) in the town is married?

Let P = population

M = males; F= females

Obviously M+F = P

Setting an equality, I get:

2/3*M + 3/5*F = P – (1/3*M + 2/5*F)

By using the LCD (15):

10M + 9F = 15P- (5M + 6F)

Collecting terms and simplifying gives back the original M+F = P

Intuitively it seems that:

2/3M + 3/5Fwould provide the fraction or per cent of the town’s married people.

P

Assuming this is correct, is there a better equation that relates more directly to the fraction of the town’s population that is married?

By substituting arbitrary numerical values for each of the variables, I obtain ~ 0.63 or 63/100 of the town being married. But is their a more appropriate way of algebraically stating this?

Any help will be appreciated.