AboutAbe Mantell Expertise Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
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}
