Question

A ​6000-seat theater has tickets for sale at ​$26 and ​$40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of ​$​185,400?

Answer 1

Answer:

x = number of tickets sold for $26 = 3900 tickets

y = number of tickets sold for $40 = 2100 tickets

Step-by-step explanation:

A ​6000-seat theater has tickets for sale at ​$26 and ​$40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of ​$​185,400?

Let

x = number of tickets sold for $26

y = number of tickets sold for $40

x + y = 6000

x = 6000 - y

$26 × x + $40 × y= $185, 400

26x + 40y = 185400

Substitute

26(6000 - y) + 40y = 185400

156000 - 26y + 40y = 185400

Collect like terms

- 26y + 40y = 185400 - 156000

14y = 29400

y = 29400/14

y = 2100 tickets

x = 6000 - y

x = 6000 - 2100

x = 3900 tickets

Hence

x = number of tickets sold for $26 = 3900 tickets

y = number of tickets sold for $40 = 2100 tickets