Question

a -seat theater has tickets for sale at $ and $. how many tickets should be sold at each price for a sellout performance to generate a total revenue of $?

Answer 1

To generate a total revenue of $187500 for a sellout performance in a theater with 6000 seats, 3500 tickets should be sold at $25 and 2500 tickets should be sold at $40.

Step-by-step explanation:

To find out how many tickets should be sold at each price for a sellout performance to generate a total revenue of $187500, we need to set up a system of equations.

Let x be the number of tickets sold at $25 and y be the number of tickets sold at $40.

Based on the given information, we can set up the following equations:

1. x + y = 6000 (equation 1)
2. 25x + 40y = 187500 (equation 2)

We can solve this system of equations using the substitution method or the elimination method.

Using the substitution method, we can solve equation 1 for x and substitute it into equation 2:

1. x = 6000 - y
2. 25(6000 - y) + 40y = 187500
3. 150000 - 25y + 40y = 187500
4. 15y = 37500
5. y = 2500

Substituting this value of y into equation 1, we can find the value of x:

1. x + 2500 = 6000
2. x = 3500

Therefore, 3500 tickets should be sold at $25 and 2500 tickets should be sold at $40.

Complete question:

a theater with 6000 seats has tickets for sale $25 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $187500?