SOLUTION: A movie theater sold a total of 440 tickets for $3940. Each regular ticket costs $5, each premium ticket costs $15 and each elite ticket costs $25. The number of regular tickets wa
Question 828134: A movie theater sold a total of 440 tickets for $3940. Each regular ticket costs $5, each premium ticket costs $15 and each elite ticket costs $25. The number of regular tickets was 3 times the number of premium and elite tickets combined. How many of each type of tickets were sold? Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website! ---
x = regular tickets
y = premium tickets
z = elite tickets
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x + y + z = 440
5x + 15y + 25z = 3940
x = 3(y + z)
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put the system of linear equations into standard form:
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x + y + z = 440
5x + 15y + 25z = 3940
x - 3y - 3z = 0
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solution:
x = regular tickets = 330
y = premium tickets = 46
z = elite tickets = 64
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system matrix
1 1 1
5 15 25
1 -3 -3
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inverse of system matrix
0.75 0 0.25
1 -0.1 -0.5
-0.75 0.1 0.25
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determinant of system matrix = 40
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