SOLUTION: A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children under 12 years old. A total of 278 tickets were sold for one showing with a total revenue of $130

Algebra ->  Matrices-and-determiminant -> SOLUTION: A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children under 12 years old. A total of 278 tickets were sold for one showing with a total revenue of $130      Log On


   

Question 994099: A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children under 12 years old. A total of 278 tickets were sold for one showing with a total revenue of $1300. If the number of adult tickets sold was 10 less than twice the number of students tickets, how many of each type of tickets were sold for the showing?
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39618) About Me  (Show Source):
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a adults
s students
c children
a=-10%2B2s
-
system%28a%2Bs%2Bc=278%2C6a%2B3.5s%2B2.5c=1300%2Ca=2s-10%29

Multiply the members of the revenue equation by 2:
system%28a%2Bs%2Bc=278%2C12a%2B7s%2B5c=2600%2Ca=2s-10%29
Three linear equations in three unknowns. Solve.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children under 12 years old. A total of 278 tickets were sold for one showing with a total revenue of $1300. If the number of adult tickets sold was 10 less than twice the number of students tickets, how many of each type of tickets were sold for the showing?
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Equations:
a + s + t = 278 tickets
6a +3.5s + 2.5t = 1300
a = 2s-10
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Modify::
a + s + t = 278
60a + 35s + 25t = 13000
a - 2s + 0 = -10
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Use any method to get:
a = 150
s = 80
t = 48