Expert: Abe Mantell - 8/12/2009

Question
I'm trying to convert the following problem into a Matrix to solve by calculator (the solving part is not the problem). Can you help?

A basketball fieldhouse seats 15,000. Courtside seats cost $12, endzone seats cost $9, and balcony seats cost $6. The total revenue for a sellout is $80,000. If half the courtside seats, half the balcony seats, and all the endzone seats are sold, then the total revenue is $50,000. How many of each type of seats are there?

Your help would be greatly appreciated.

Answer
Hello Ann,


Let x=# of courtside seats sold,
let y=# of endzone seats sold, and
let z=# of balcony seats sold.

Thus, we get the following equations:
1. x + y + z = 15,000 (the total # of tickets sold)
2. 12x + 9y + 6z = 80,000 (total revenue)
3. 12(x/2) + 9y + 6(z/2) = 50,000 (the last criteria you gave)

Thus all we need to do is solve the system:
x+y+z=15000
12x+9y+6z=80000
6x+9y+3z=50000

The trouble is the solution does not make sense!
Aside from fractional values, x turns out to be negative!!!
{x = -25000/9, y = 20000/9, z = 140000/9}

Are you sure the problem is correctly stated?

TTYL, Abe