Whilst revising, a problem caught my eye and I cannot seem to find an answer. I am usually bad at these types of questions.
On a certain Russian-American committee, $\frac23$ of members are men, and $\frac38$ of the men are Americans. If $\frac35$ of the committee members are Russians, what fraction of the members are American women?
A. $\frac{3}{20}$ B. $\frac{11}{60}$ C. $\frac{1}{4}$ D. $\frac{2}{5}$ E. $\frac{5}{12}$
Could you please explain how to approach and analyse the problem, maybe give some hints or the complete procedure of solving?
I get a bit confused with all those fractions. What I tried was to convert them to percentages but that seemed a bad idea.
Sorry if this question is annoying.
Thank you.
Update: I solved the problem both intuitively and mathematically. Thanks.
Best Answer
Let me try. We will pick a nice number for the total number of members so that every category of members come out whole numbers. We can pick the least common multiple of all the denominators of the fractions. That gives us $120.$ Of course as long as we are only interested in the ratio, it don't matter what that number is. It makes computation easier to do.
Suppose there were $120$ members. There are $80$ men and $40$ women. Of the $80$ men $30$ are American and $50$ russian. There are $72$ Russians on the committee that leave $22$ Russian women and $18$ American women on the committee. The fraction of American women on the committee is $$\frac{18}{120} = \frac3{20}.$$
Hopefully I did not make any silly arithmetic errors.