Question

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.

Answer 1

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