Problema Solution
A Broadway theater has 700 seats, divided into orchestra,main and balcony seating. Orchestra seats sell for $40, main seats sell for $25, and balcony seats for $20. If all the seats are sold, the gross revenue to the theater is $18,450. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $15,650. How many are there of each kind of seat?
Answer provided by our tutors
let
o = the number of orchestra seats
m = the number of main seats
b = the number of balcony seats
Broadway theater has 700 seats
o +m + b = 700
if all the seats are sold the gross revenue to the theater is $18,450
40o + 25m + 20b = 18450
if all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $15,650
40(o/2) + 25m + 20b = 15650
by solving the system of equations
o +m + b = 700
40o + 25m + 20b = 18450
40(o/2) + 25m + 20b = 15650
we find
o = 140 orchestra seats
m = 330 main seats
b = 230 balcony seats
click here to see the step by step solution of the system of equations
there are 140 orchestra seats, 330 main seats and 230 balcony seats.