2731 tickets should be sold at $27 and 2269 tickets should be sold at $40.
Given that,
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 total revenue of $154,500 is to be determined.
Here,
Let the number of seats sold for $27 be x and for $40 be y
For a 5000-seat theater
x + y = 5000
x = 5000 - y - - - - - - (1)
Total revenue generated is $154,500 by selling x tickets at $27 and y tickets at $40.
27x +40y = 154,500 - - - - - - (2)
Solving equations 1 and 2
27(5000 - y )+ 40y = 154,500
125,000- 27y + 40y = 154,500
13 y = 29500
y =2269
Putting y in equation 1
x = 5000 - 2269
x = 2731
Thus, 2731 tickets should be sold at $27 and 2269 tickets should be sold at $40.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ1
