system of equations application

Question

a 1200-seat theater sells two types of tickets for a concert. Premium seats sell for $40 each and regular seats sell for $20 each. At one event $36,320 was collected in ticket sales with 20 seats left unsold. How many of each type of ticket was sold.

Answer 1

Let x = number of premium seats sold

Let y = number of regular seats sold

Total number of seats sold = 1200 - 20 = 1180

Sales from premium tickets = 40x (price of ticket x number of seats)

Sales from regular tickets = 20y

Thus the following system of equations can be set up:

x + y = 1180 -------------------(1)

40x + 20y = 36320 ----------(2)

Let us use the method of elimination to solve the system:

Multiply equation (1) by -20 to get

-20x - 20y = - 23600 -------------(3)

Add equations (2) and (3) to get

20x = 12720

x = 12720/20

x = 636

Using equation (1), y = 1180 - 636 =544

Solution: Premium tickets sold = 636; Regular tickets sold = 544