Problema Solution
The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $38, balcony tickets are $33, and mezzanine tickets are $31. One particular night, sales totaled $72,299. There were 15 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 61 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold?
Answer provided by our tutors
let
x = the number of main floor tickets sold
y = the number of balcony tickets sold
z = the number of mezzanine tickets sold
Main floor tickets are $38, balcony tickets are $33, and mezzanine tickets are $31. One particular night, sales totaled $72,299:
38x + 33y + 31z = 72299
There were 15 more main floor tickets sold than balcony and mezzanine tickets combined:
x = y + z + 15
The number of balcony tickets sold is 61 more than 3 times the number of mezzanine tickets sold:
y = 61 + 3z
by solving the system of equations:
38x + 33y + 31z = 72299
x = y + z + 15
y = 61 + 3z
we find:
x = 1031 main floor tickets
y = 778 balcony tickets
z = 239 mezzanine tickets
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