A 6000-seat theater has tickets for sale at $28 and $40. How many tickets should be sold at each price for a sellout show to generate a total revenue 194400

The number of tickets for sale at $28 should be

The number of tickets for sale at $40 should be

3,833 for $28

2167 for $40

Step-by-step explanation:

Let X be the number of tickets sold at the price of $24, And Y be the number of tickets sold at the price of $40.

Now, $ 28X will be the revenue generated due to the $28 tickets

And, $40Y will be the revenue generated due to the 40$ tickets.

Now, Total revenue generated should be $194400.

Thus, 28X + 40Y = 194400 - (1).

Also,

Total number of seats in theater is 6000.

So, X + Y = 6000. - (2)

X = 6000 - Y.

Put in equation 1

We get, 168,000 - 28Y + 40Y = 194,400

12Y = 26,000

Y = 2,166.66

Since, Y is of 40 $ so minimum tickets sold should be 2167.

X = 3,833.