SOLUTION: A theater charges $8 for adults, $4.50 for children, and $6 for senior citizens. If yesterday 405 tickets were sold, $2320 wss collected, and the number of children's tickets were

Question 196215: A theater charges $8 for adults, $4.50 for children, and $6 for senior citizens. If yesterday 405 tickets were sold, $2320 wss collected, and the number of children's tickets were twice the adult's tickets how many were sold of each type?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A theater charges $8 for adults, $4.50 for children, and $6 for senior citizens.
If yesterday 405 tickets were sold, $2320 was collected, and the number of
children's tickets were twice the adult's tickets how many were sold of each type?
:
Three types of tickets sold; their number represented by; a, s, c
:
Write an equation for each statement:
"If yesterday 405 tickets were sold,"
a + s + c = 405
:
"$2320 was collected,"
8a + 6s + 4.5c = 2320
:
"the number of children's tickets were twice the adult's tickets"
c = 2a
:
In the first two equations, replace c with 2a, simplify as much as you can:
a + s + 2a = 405
3a + s = 405
s = (405 - 3a)
and
8a + 6s + 4.5(2a) = 2320
8a + 6s + 9a = 2320
17a + 6s = 2320
;
Replace s with (405-3a) in the above equation, find a
17a + 6(405-3a) = 2320
17a + 2430 - 18a = 2320
17a - 17a = 2320 -2430
-a = -110
a = +110 adult tickets
:
Find s: (s = 405 - 3a)
s = 405 - 3(110)
s = 405 - 330
s = 75 Senior tickets
:
Use the 1st equation to find c:
110 + 75 + c = 405
c = 405 - 185
c = 220 children tickets
:
:
Check solutions in the total$ equation
8(110) + 6(75) + 4.5(220) =
880 + 450 + 990 = 2320; confirms our solutions
:
how many were sold of each type?
110 adults, 75 seniors, 220 children
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