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 89427: 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?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
Let a = no. of adults, c = no. of children, s = no. of seniors
:
Write an equation for each statement:
:
"The total ticket sales were $1920. "
12a + 4c + 7s = 19
:
"There were 50 more adult tickets sold than children's tickets,"
a = c + 50
:
"the number of senior citizen's tickets were 4 times the number of children's tickets."
s = 4c
:
How many tickets were sold?
:
Using the 1st eq (12a + 4c + 7s = 1920) substitute (c+50) for a and 4c for s:
12(c+50) + 4c + 7(4c)c = 1920
:
12c + 600 + 4c + 28c = 1920
:
12c + 4c + 28c = 1920 - 600
:
44c = 1320
:
c = 1320/17
:
c = 30 children
:
Use the other two equations to determine no. of adults and seniors
:
Check solutions by substitution in the 1st equation
;
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