Why use a "system of equations", all the variables are easily defined .
number of mezzanines --- x
number of balconies ----- 3x + 78
number of main floor ---- x + 3x+78 + 435
= 4x + 513
59(4x+513) + 50(3x+78) + 40x = 73785
426x + 34167 = 73785
x = 93
back-sub into my definitions
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 $59, balcony tickets are $50, and mezzanine tickets are $40. One particular night, sales totaled $73,785. There were 435 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 78 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold?
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