At a movie, 1/4 of the people in the theater were men, 5/8 were woman l, and the rest were children. If there were 100 more woman than children, what was the total number of people in the theater.
Let x---------------> number of men in the theater y---------------> number of women in the theater z---------------> number of children in the theater T--------------> total number of persons in the theater
we know that T=x+y+z x=(1/4)*T y=(5/8)*T----------> equation 1 z=T-[(1/4)*T+(5/8)*T]-----> z=T-(7/8)*T------> z=(8*T-7*T)/8------> z=(1/8)*T z=(1/8)*T----------> equation 2
y=100+z--------> equation 3 I substitute (1) and (2) in (3) (5/8)*T=100+(1/8)*T------> (5/8)*T-(1/8)*T=100--------> T=200 persons
the total number of people in the theater was 200 persons number of men in the theater------> 200*(1/4)=50 men number of women in the theater----> 200*(5/8)=125 women number of children in the theater----> 200*(1/8)=25 children
