Question

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

Answer 1

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