Answer:
Let´s define the variables:
x = number of people in theater A
y = number of people in theater B
We know that a 20% (or 0.2 in decimal form) of the people in theater A answered the survey, then the number of people from theater A that answered the survey is: Na = 0.2*x
We know that a 30% (or 0.3 in decimal form) of the people in theater B answered the survey, then the number of people from theater B that answered the survey is: Nb = 0.3*y
There where 800 people in total (counting from the two theatres)
Then x + y = 800.
A) In this case we have:
Na = Nb
this means that:
0.2*x = 0.3*y
and we also have the equation:
x + y = 800
To solve this, we need to isolate one variable in one of the equations, i will isolate x in the second equation:
x = 800 - y
And now we can replace this in the other equation to get:
0.2*(800 - y) = 0.3*y
We need to solve this for y:
160 - 0.2*y = 0.3*y
160 = 0.3*y + 0.2*y = 0.5*y
160/0.5 = y = 320
Then there where 320 people in theater B, and:
x + y = 800
x + 320 = 800
x = 800 - 320 = 480
There where 480 people in theather A.
B) Now we have:
x = 440
y = 360
then:
Na = 0.2*440 = 88
In theater A, 88 people answered the survey.
Nb = 0.3*360 = 108
In theater B, 108 people answered the survey.
In total, 88 + 108 = 196 people answered the survey.
