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

Question 86218: Tickets for an event cost $4 for children, $12 for adults, and $ 7 for senior citizens. The total ticket sales were $ 1920. There wee 50 more adult tickets sold than child tickets, and the number of senior citizen tickets wre 4 time 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 citizen tickets were 4 times the number of child tickets. How many of each ticket were sold.
:
Let a = number of adult tickets sold
Let s = number of senior tickets sold
Let c = number of children's tickets
:
Translate each statement to an equation:
:
"The total ticket sales were $ 1920. "
12a + 7s + 4c = 1920
:
"There were 50 more adult tickets sold than child tickets,"
a = (c + 50)
:
"the number of senior citizen tickets were 4 times the number of child tickets."
s = 4*c
:
Substitute ((c+50) for a and 4c for s in the 1st equation, find c:
12(c+50) + 7(4c) + 4c = 1920
:
12c + 600 + 28c + 4c = 1920
:
12c + 28c + 4c = 1920 - 600
:
44c = 1320
:
c = 1320/44
:
c = 30 children
:
Now use the equations you have to find the number of adults and seniors
:
Substitute your values a, s, and c in the 1st equation to check your solutions
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