A 6000 seat theater has tickets for sale at $27 and $40 how many tickets should be sold at each price for a cello performance to generate a total revenue of $182,800?
- BryceLv 71 month ago
x + y= 6000 or y= 6000 - x
27x + 40(6000 - x)= 182,800
-13x= -57,200; x= 4400, y= 1600
- 1 month ago
A cheeky way to answer this is to do the maximum profit (40*6000=240,000) minus the desired profit (240,000-182,800=57,200) which is your excess profit. Now the difference in ticket prices is (40-27=13) 13 dollars so how many differences in seat prices can you fit in your excess profit (57,200/13=4,400) this means 4,400 seats can be the cheaper ticket and still be at the desired profit. This means 1,600 seats should be $40 and 4,400 should be $27.