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 + 3/5F would provide the fraction or per cent of the town’s married people.
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.