Question

A 1400-seat theater sells two types of tickets for a concert. Premium seats sell for $30 each and regular seats sell for $20 each. At one event $33,950 was collected in ticket sales with 10 seats left unsold. How many of each type of ticket was sold?

Answer 1

premium seats sold : 638
Regular seats sold: 552

Answer 2

x = 638

y = 1190 - 638 = 552

Explanation:

Let x = premium seats

let y = regular seats

x + y = 1190 (ten were not sold

30x + 20y = 30180 (amount collected

now multiply the first equation by 20 and subtract

20x + 20y = 23800

30x + 20y = 30180

-10x = -6380

x = 638

y = 1190 - 638 = 552

check it by multipying x and y by their price to see if you come up with the correct amount

Hope this helps