Question 909632: An outdoor amphitheater has 25,000 seats. Ticket prices are $15, $17, and $25 and the number of tickets priced at $17 must equal two times the number priced at $25 How many tickets of each type should be sold (assuming all seats can be sold) to bring in $434,500? Set up a system of equations and solve using inverse matrix method.
a) Declare your variables
b) Write the equations associated with the above problem:
x+y+z=25000
15x+17y+25z=434500
y=2z
c) Write the matrix equation associated with the above problem
d)Use matrix algebra to find the number of tickets
e) If you change the ticket prices to $8, $12, and $20 and now must bring in $256,000, the new solution is:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! a)
x=$15 tickets
y=$17 tickets
z=$19 tickets
b)
x+y+z=25000
15x+17y+25z=434500
y=2z
c)
1,1,1,25000
15,17,25,434500
0,1,-2,0
d)
(12,250;8,500;4,250)
1,0,0,12250 x
0,1,0,8500 y
0,0,1,4250 z
e)
1,1,1,25000
8,12,20,256000
0,1,-2,0
1,0,0,16600 x $8
0,1,0,5600 y $12
0,0,1,2800 z $20
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