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 $145,400?

Answer 1

To generate a total revenue of $145,400 for a sellout performance in a 5000-seat theater with tickets priced at $26 and $40, 3,900 tickets should be sold at $26 each and 1,100 tickets should be sold at $40 each.

Step-by-step explanation:

To find the number of tickets that should be sold at each price, we need to set up a system of equations based on the total revenue and the number of tickets sold at each price. Let x represent the number of $26 tickets and y represent the number of $40 tickets. The total revenue equation is 26x + 40y = 145,400. We also know that the total number of tickets sold should be equal to the total seating capacity of the theater (5000): x + y = 5000. Now we can solve this system of equations to find the values of x and y.

Multiplying the second equation by 26 gives us 26x + 26y = 130,000. Subtracting this equation from the first equation eliminates the x term: 26x + 40y - (26x + 26y) = 145,400 - 130,000. Simplifying this equation gives us 14y = 15,400. Dividing both sides by 14 gives us y = 1,100. Substituting this value into the second equation gives us x + 1,100 = 5000. Solving for x gives us x = 3,900.

Therefore, 3,900 tickets should be sold at $26 each and 1,100 tickets should be sold at $40 each for a sellout performance to generate a total revenue of $145,400.

Answer 2

let x - number of $26 tickets

y- number of $40 tickets

x + y = 5000

x = 5000 - y

26x + 40y = 155,200

26(5000 - y) + 40y = 155200

130,000 - 26y + 40y = 155200

14y = 25,200

y = 1800

x = 5000 - 1800 = 3200