A Broadway theater has 500 seats divided into orchestra main

A Broadway theater has 500 seats, divided into orchestra, main floor, and balcony seating. Orchestra seating sells for $50, main floor seating sells for $35, and balcony seating sells for $25. If all the seats are sold the gross receipts for the night are $17,100. If all the main floor seating and balcony seating are sold but only half the orchestra seating is sold, the gross receipts are $14,600. How many seats of each kind are in the theater?

Solution

o + m + b = 500 50o + 35m + 25b = 17100 25o + 35m + 25b = 14600 25o = 17100-14600 = 2500 o = 100 100 + m + b = 500 50 * 100 + 35m + 25b = 17100 35m + 25b = 12100 m+b = 400 25m + 25b = 10,000 35m + 25b = 12100 10m = 12,100-10,000 = 2100 m = 210 b = 190