Question

A 5000​-seat theater has tickets for sale at ​$26 and ​$40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of ​$149 comma 600​?

Answer 1

3,600 from $26 tickets and 1,400 from $40 tickets.

Explanation:

Let x = number of $26 tickets and y= number of $40 tickets

x + y = 5000 ⇒ x = 5000 - y

26x + 40y = 149,600

26(5000 - y) + 40y = 149600

130,000 - 26y + 40y = 149600

14y = 19600

y = 19600/14 = 1,400

x = 5000 - 1400 = 3,600

So, 3,600 from $26 tickets and 1,400 from $40 tickets.