Percent of older women?

Question

If 1/3 of people are elderly men and 2/8 are young women, what percent of people is older women? The answer should be 41%, but I am not sure how to get that answer. I did add the fractions together, getting an LCD of 24 first. So, the fractions would now be 8/24 and 6/24, giving me a total fraction of 14/24, which can be reduced to 7/12. But I am not sure where to go from there, or if those steps are necessary in solving the problem. 

Answer 1

x = fraction that consists of older women

x = 1 - (1/3 + 2/8) = 1 - (1/3 + 1/4) = 1 - (4/12 + 3/12) = 1 - 7/12

x = 12/12 - 7/12 = 5/12

The fraction is 5/12. Get the percent p from the proportion:

5/12 = p/100

p = 100(5/12) = 41.67% (with roundoff)