OpenStudy (anonymous):
A 2000 seat theater has tickets for sale at $15 and $22. How many tickets should he sold at each price for a sellout performance to generate a total revenue of$33,500?
OpenStudy (shinalcantara):
Let 'x' be the number of tickets @ $15 'y' be the number of tickets @ $22 ----------------------------------- Since the total tickets that he can sell is 2000 then x + y = 2000 ----equation 1 ----------------------------------- The total revenue amounts to $33,500 15x + 22y = 33,500 -----equation 2 ----------------------------------- Multiply equation 1 with 15 (x + y = 2000) x15 15x + 15y = 30,000 ----equation 1' ----------------------------------- Subtract equation 1' from equation 2 15x + 22y = 33,500 - 15x + 15y = 30,000 7y = 3,500 y = 500 ----------------------------------- Substitute y=500 to equation 1 x + y = 2000 x + 500 = 2000 x = 2000 - 500 x = 1,500
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