The local theater has three types of seats for Broadway play

The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $55, balcony tickets are $33, and mezzanine tickets are $28. One particular night, sales totaled $69,915. There were 363 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 55 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold?

Solution

Let number of main ticket be x, balcony ticket be y and mezzanine ticket be z

55x+33y+28z=69915

x=y+z+363

y=3z+55

solving these three equations we get

x=938, y=445, z=130