Question 82389: Tickets for an event cost $5 for children, $10 for adults, and $8 for senior citizens. The total ticket sales were $2060. There were 50 more adult tickets sold than child tickets, and the number of senior citizens tickets were 3 times the number of child tickets. How many of each ticket were sold?
Hint: You must find all 3 numbers to earn full credit.
Answer:
Child tickets: _________ sold
Adult tickets: _________ sold
Senior citizen tickets: _________ sold
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! x = no. of children; y = no. adults; z = no. of seniors
:
Write an equation for each sentence
Tickets for an event cost $5 for children, $10 for adults, and $8 for senior citizens.
"The total ticket sales were $2060. "
5x + 10y + 8z = 2060
:
"There were 50 more adult tickets sold than child tickets,"
y = x + 50
:
"the number of senior citizens tickets were 3 times the number of child tickets"
z = 3*x
:
. How many of each ticket were sold?
:
Notice that the last two equation put both y and z in terms x. Therefore if
we substitute for y and z in the total sales equation we can find x:
5x + 10(x+50) + 8(3x) = 2060
:
5x + 10x + 500 + 24x = 2060; multiplied what's in brackets
:
5x + 10x + 24x = 2060 - 500; subtracted 500 from both sides
:
39x = 1560
:
x = 1560/39
:
x = 40 children
:
Then:
y = x + 50
y = 40 + 50
y = 90 adults
:
And
z = 3*x
z = 2*40
z = 120 seniors
:
Check our solutions in the total sales equation:
5(40) + 90(10) + 8(120) =
200 + 900 + 960 = 2060
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