SOLUTION: Tickets for an event cost $4 for children, $12 for adults, and $7 for senior citizens. The total ticket sales were $1920. There were 50 more adult tickets sold than child tickets

Question 57507: Tickets for an event cost $4 for children, $12 for adults, and $7 for senior citizens. The total ticket sales were $1920. There were 50 more adult tickets sold than child tickets, and the number of senior citizens tickets were 4 times the number of child tickets. How many of each ticket were sold?
I could really use some help. Thanks
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each statement:
Let c = no. of children; a = no. of adults; s = no. of seniors
"Tickets for an event cost $4 for children, $12 for adults, and $7 for seniors.
The total ticket sales were $1920."
4c + 12a + 7s = 1920
:
"There were 50 more adult tickets sold than child tickets,"
a = c + 50
:
"the number of senior citizens tickets were 4 times the number of child tickets.:
s = 4c
:
How many of each ticket were sold?
:
Remember the 1st equation: 4c + 12a + 7s = 1920
Substitute(c+50) for a, and 4c for s:
:
4c + 12(c+50) + 7(4c) = 1920
4c + 12c + 600 + 28c = 1920
44c = 1920 - 600
44c = 1320
c = 1320/44
c = 30 children
:
Use the adult and the senior equations to find the value of a and s, then check your 3 solutions in the 1st equation.

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