Question

At a club dinner, every member brought 1 or 2 guests. If the ratio of the number of members to the number of guests was 3 : 5, what fraction of the members who brought 2 guests each?

Answer 1

Suppose there are x members with a guest.
y members with two guests.
(x + y)/(x + 2y) = 3/5
5(x + y) = 3(x + 2y)
5x + 5y = 3x + 6y
2x = y
x:y = 1:2
y/(x + y) = 2/(1 + 2) = 2/3
So the fraction of the members who bought 2 guests each is 2/3.