how many seats should he have in each section?

Question

A theater owner wants tot divide an 1800 seat theater into three sections, with tickets costing $20, $35 and $50, depending on the section. he wants to have twice as many $20 tickets as the sum of the other tickets, and he wants to earn $48,000 from a full house. To find how many seats he should have in each section, solve the system of equations 

x+y+z=1800

x=2(y+z)

20x+35y+50z=4800

 

where x, y, and zz are the numbers of $20 tickets, $35 tickets and $50 tickets, respectively.

Answer 1

Using TI-84 calculator, set up the following matrix A.

2ND X^-1

EDIT 3 X 4, enter your numbers

2ND QUIT

2ND X^-1

MATH B

2ND X^-1 

ENTER

 

1       1       1       1800

1      -2      -2          0                   = A

20     35      50     48000

 

Use rref([A]) and get x=1200, y=400, and z=200