SOLUTION: I need to set up the 3 by 3 systems of linear equations and solve for them on the following word problem. A theater has 500 seats divided into orchestra, main, and balcony seati

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I need to set up the 3 by 3 systems of linear equations and solve for them on the following word problem. A theater has 500 seats divided into orchestra, main, and balcony seati      Log On


   

Question 155943: I need to set up the 3 by 3 systems of linear equations and solve for them on the following word problem.
A theater has 500 seats divided into orchestra, main, and balcony seating. Orchestra seats sell for $50, main seats for $35, and balcony seats for $25. If all seats are sold, the revenue is $17,100. If all the main and balcony seats are sold, but only half the orchestra seats, the revenue is $14,600. How many are there of each kind of seat?
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
THE THREE EQUATIONS ARE:
O+M+B=400
50*O+35*M+25*B=17,100
50*O/2+35*M++25*B=14,600