A 6000 -seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of

Question

A 6000 -seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $185,600? PLEASE HELP ME

Answer 1

N = number of tickets sold at $24 each

M = number of tickets sold at $40 each

(i) 24N + 40M = 185,600
(ii) N + M = 6000

(ii) ⇒ M = 6000 - N

Plug into (i) and get

24N + 40(6000 - N) = 185,600

Solve for N, then plug the solution into either (i) or (ii) to get M.

 

You should get

 

N = 3400

M = 2600