Answer:
Let's define the variables:
A = number of seats in section A.
B = number of seats in section B.
C = number of seats in section C.
We have the equations:
A + B + C = 45,000.
C - 300 = B/2
A*$28 + B*$24 + C*$20 = $1,139,200
This is a system of equations, the first step to solve this is to isolate one variable in one of the equations, and then replace it in the others.
I will isolate C in the second equation:
C = B/2 + 300.
Now let's replace this in the other two equations:
A + B + B/2 + 300 = 45,000
A*$28 + B*$24 + (B/2 + 300)*$20 = $1,139,200
Let's simplify these equations:
A + B*(3/2) = 44,700
A*$28 + B*$34 + $6,000 = $1,139,200
Now let's isolate A in the first equation:
A = 44,700 - B*(3/2)
Let's replace this in the other equation:
(44,700 - B*(3/2))*$28 + B*$34 + $6,000 = $1,139,200
Now let's solve this for B.
-B*$8 + $1,252,200 = $1,139,200
-B*$8 = $1,139,200 - $1,252,200 = -$113,000
B = $113,000/8 = 14,125
Now we can replace that in the equations:
A = 44,700 - B*(3/2) = 44,700 - 14,125*(3/2) = 23,512.5, that we should round up to 23,513.
And C = B/2 + 300 = 7362.5
As we rounded the previous one up, we should round this one down to 7362.
