Problema Solution
The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $58, Balcony tickets are $44, and mezzanine tickets are $37. One particular night, sales totaled $82,812. There were 79 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 333 more than 4 times the number of mezzanine tickets sold. How many of each type of tickets were sold?
Answer provided by our tutors
let 'x' represent the number of mezzanine tickets sold, then '4x+333' represents the number of balcony tickets sold and (x+4x+333+79) represents the number of main floor tickets sold
82812 = 37x + 44(4x+333) + 58(x+4x+333+79)
solving for 'x' we have x=88
4*88 + 333 = 685
685+79 = 764
there were 88 mezzanine tickets sold, 685 balcony tickets sold and 764 main floor tickets sold