The local theater has three types of seats for broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $50, balcony tickets are $44, and mezzanine tickets are $35. One particular night, sales totaled $52,411. There were 386 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 36 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold?
a) 147 main floor, 81 balcony, 104 mezzanine
b) 178 main floor, 92 balcony, 114 mezzanine
c) 212 main floor, 105 balcony, 131 mezzanine
d) 246 main floor, 118 balcony, 148 mezzanine