A 6000-seat theater has tickets for sale at $25 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $174,000?

Step-by-step explanation:

Let x be the amount of tickets sold for $25 and y be the amount of tickets sold for $40, since there are 6000 seats theatre then;

x+y = 6000 1

If x tickets cost $25 and y tickets are sold for $40 with total revenue of $174,000, then;

25x + 40y = 174,000 2

From 1, x = 6000-y 3

Substitute equation 3 into 2:

25x + 40y = 174,000.

25(6000-y) + 40y = 174,000

150,000-25y + 40y = 174,000

150,000+15y = 174,000

15y = 174,000-150,000

15y = 24,000

y = 24,000/15

y = 1600

Substitute y = 1600 into equation 3:

x = 6000-y

x = 6000-1600

x = 4400

Hence 4400 $25 tickets and 1600 $40 tickets must be sold to generate a revenue of $174,000

40 minutes

step-by-step explanation:

add the time and multiply by 2