Fraction Word Problem

Question

In a community, 2/3 of all of the men are married to 3/5 of all of the women.  What fraction of the entire community is married?

 

Help!  I can't figure out how to do this.  I keep thinking 2/3x + 3/5y has to be the final answer.  But I think they want 1 fraction as an answer.

Answer 1

m = number of men

w = number of women

 

Assuming that each man is married to only one woman, and each woman is married to only one man,

 

(2/3)m = (3/5)w       Multiply by LCD, 15

10m = 9w                The smallest values for which this is true

 

m = 9, w = 10

 

Check:

 

(2/3)9 = (3/5)10

 

So the community has at least 19 people. 12 are married (six men and six women). 

The fraction is 12/19