# Theater Revenue Math Problem?

A theater has 600 seats, divided into orchestra, main floor, and balcony seating. Orchestra seats sell for \$80, main floor seats for \$60 and balcony seats for \$25. If all the seats are sold, the total revenue to the theater is \$33,500. One evening, all the orchestra seats were sold, 3/5th of the main seats were sold, and 4/5th of the balcony seats were sold. The total revenue collected was \$24,640. How many are there of each kind of seat?

Relevance

o + m + b = 600

80o + 60m + 25b = 33500

80o + 60*(3/5)*m + 25*(4/5)*b = 24640, i.e. 80o + 36m + 20b = 24640

Subtract those last two equations:

24m + 5b = 8860, call that equation 4

Multiply the first equation by 80:

80o + 80m + 80b = 48000

Subtract the second equation from that:

20m + 55b = 14500, call that equation 5

Multiply equation 4 by 11:

264m + 55b = 97460

Subtract equation 5 from that:

244m = 82960

m = 82960/244

m = 340

Substitute that into equation 4:

24m + 5b = 8860

24(340) + 5b = 8860

8160 + 5b = 8860

5b = 8860 - 8160

5b = 700

b = 700/5

b = 140

Substitute m and b into equation 1:

o + 340 + 140 = 600

o = 600 - 340 - 140

o = 120