Use a system of equations to solve the following problem. The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $56, balcony tickets are $38, and mezzanine tickets are $30. One particular night, sales totaled $65,524. There were 109 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 178 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold?

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