SOLUTION: The Forrest Theater can seat a total of 360 people. They take in $15,150 when every seat is sold. If orchestra section tickets cost $45 and balcony cost $35, find the number of sea

Question 1102773: The Forrest Theater can seat a total of 360 people. They take in $15,150 when every seat is sold. If orchestra section tickets cost $45 and balcony cost $35, find the number of seats in the orchestra and the number of seats in the balcony.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

represent the number of orchestra tickets and let

represent the number of balcony tickets.
The total number of tickets is 360, so

.
The total value of the orchestra tickets is

dollars and the total value of the balcony tickets is

dollars. So the total box office take must be the sum of the value of the orchestra tickets and the value of the balcony tickets, to wit:

You now have a 2 X 2 system of equations that can be solved by either substitution or elimination.

Alternatively, you could have recognized that if

is the number of orchestra tickets, then the number of balcony tickets must be

, and since orchestra tickets are worth $45 and balcony tickets are worth $35, the total value of all the tickets must be

.

All that is necessary is to solve for

and then calculate

You might want to compare this alternative method to the substitution method of solving the 2X2 system.

John

My calculator said it, I believe it, that settles it

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