At a movie, 1/4 of the people in the theater were men, 5/8 were woman, and the rest were children. if there were 100 more women than children, what was the total number of people in the theater?

Men : women : children = (2/8) : (5/8) : (1/8) = 2:5:1
The difference between the ratio units of women and childre is 5-1=4, which is half the total number of ratio units (8). Thus 100 people are half the total number of people in the theater.

The total number of people in the theater was 200.