SOLUTION: Movie tickets cost $5 for children, $8 for adults and $4 for seniors. The theater earned $1890 in a day. Five times as many adults attended as seniors. Twice as many children atten

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Question 419823: Movie tickets cost $5 for children, $8 for adults and $4 for seniors. The theater earned $1890 in a day. Five times as many adults attended as seniors. Twice as many children attended as seniors. Set up and solve a system of equations, to find how many of each type of ticket was sold.
Any help would be greatly appreciated!!
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Movie tickets cost $5 for children, $8 for adults and $4 for seniors.
The theater earned $1890 in a day. Five times as many adults attended as seniors.
Twice as many children attended as seniors.
Set up and solve a system of equations, to find how many of each type of ticket was sold.
:
Let c = no. of children
Let a = no. of adults
Let s = no. seniors
:
Write an equation for each sentence:
:
"The theater earned $1890 in a day."
5c + 8a + 4s = 1890
:
"Five times as many adults attended as seniors."
a = 5s
:
" Twice as many children attended as seniors."
c = 2s
:
5c + 8a + 4s = 1890
replace c with 2s; replace a with 5s
5(2s) + 8(5s) + 4s = 1890
10s + 40s + 4s = 1890
54s = 1890
s =
s = 35 Seniors
then
a = 5(35)
a = 175 adults
and
c = 2(35)
c = 70 children
:
:
Check solution
70(5) + 175(8) + 35(4) =
350 + 1400 + 140 = 1890; confirms our solutions