Problema Solution
A threatre has 400 seats, divided into orchestra, main, and balcony seating. Orchestra sears sell for $50, main seats for $30, and balcony seats for $25. If all the seats sre sold the gross revenue to the theatre is $13,000. if all the main and balcony seats are sold, but only hald the orchestra seats are sold, the gross revenue is $11,000. How many are there of each kind of seat?
Answer provided by our tutors
o+m+b = 400
50o + 30m + 25b = 13000
25o + 30m + 25b = 11000 (since half the orchestra seats, so half of 50 is 25)
solve the system of equations using matrices (if you need more than this just message me but it's a lot of work for only 25 cents)
o = 80, m = 200, b = 120
therefore, there are 80 orchestra seats, 200 main seats, and 120 balcony seats