SOLUTION: A theater has 650 seats. After one sell-out performance, the theater made $11,600. If orchestra seats cost $20 each and balcony seats cost $12, how many orchestra and balcony seats

Question 147413: A theater has 650 seats. After one sell-out performance, the theater made $11,600. If orchestra seats cost $20 each and balcony seats cost $12, how many orchestra and balcony seats are there in the theater?
Answer by 24HoursTutor.com(40) (Show Source): You can put this solution on YOUR website!
The total number of seats = 650
Let the number of orchestra seats be x
Let the number of balcony seats be y
So we can say that :
No. of balcony seats + no. of orchestra seats = 650
x+y = 650
x = 650-y
Now, since each orchestra seat costs 20$ each the amount collected by selling such seats would be = no. of seats X amount per seat
= x X 20
=2ox
Similiarly, each balcony seat costs 12$ so the amount collected by selling such seats would be = no. of seats X amount per seat
y x 12
=12y
Now, we know that the total money collected = 11,600 $
Therefore,
money collected by balcony seats + money collected from orchestra seats = 11,600
20x + 12y = 11,600
we can substitute x with 650-y which we got above to get
20(650-y) + 12y = 11600
13000-20y+12y=11600
-20y+12y=11600-13000
-8y = -1400
y= 1400/8
y=175
x=650-y=650-175=475
Ans.: The number of balcony seats = y = 175
The number of orchestra seats = x = 475
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