A 5000 seat theater has tickets for sale at $27 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $153,200?

Question

A 5000 seat theater has tickets for sale at $27 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $153,200?

Answer 1

40x + 27(5000-x) = 153,200

40x-27x = 153,200- 27(5000)

13x = 153,200- 135,000

x = 18,200/13

x = 1,400 tickets at $40

5000-1400 = 3,600 tickets at $27

27(3600) +40(1400)

= 97200+ 56000

= 153200

153200/5000= $30.64 average ticket price

30.64-27 = 3.64

40-30.64 = 9.36

9.36/3.64 = about 2.57 times as many $27 tickets as $40

36,000/14000 = 36/14 = 18/7 = about 2.57