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

Cthe residual plot for model 1 has a non random pattern and is a good fit for the data

Cbecause they are equal so that means it is the same on both sides? ! hope this