A 5000 seat theater has tickets at $27 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $158,400

Let

x = the number of tickets sold at $27 each

y = the number of tickets sold at $40 each

Because 5000 tickets were sold, therefore

x + y = 5000 (1)

Because the revenue generated was $158,400, therefore

27x + 40y = 158400 (2)

From (1),

y = 5000 - x (3)

Substitute (3) into (2).

27x + 40 (5000 - x) = 158400

-13x + 200000 = 158400

-13x = - 41600

x = 3200

y = 5000 - x = 5000 - 3200 = 1800

Answer:

3200 tickets at $27 each, and

1800 tickets at $40 each