SOLUTION: Tickets to a concert cost $2 for children and $5 for adults. If 630 people attended the concert and the ticket sales totaled $2,910, how many children attended the concert?

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Question 971452: Tickets to a concert cost $2 for children and $5 for adults. If 630 people attended the concert and the ticket sales totaled $2,910, how many children attended the concert?
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
make 2 equations
one for the total amount of people and one for the amount of tickets sold

x=children
y=adults

x%2By=630
there are 630 people total. you add the children and adults together to find the total.

2x%2B5y=2910
the total amount of ticket sales is the adult sales and the children sales combined.
The sales of the children tickets is the $2 times the number of tickets.
The sales of the adult tickets is the $5 times the number of tickets.

x%2By=630 can be solved for y
x-x%2By=630-x
0%2By=630-x
y=630-x
This can be used to find x in the other problem.
2x%2B5y=2910
2x%2B5%28630-x%29=2910
2x%2B%285%2A630%29%2B%285%2A%28-x%29%29=2910
2x%2B3150-5x=2910
-3x%2B3150=2910
-3x%2B3150-3150=2910-3150
-3x=-240
%28-3x%29%2F%28-3%29=%28-240%29%2F%28-3%29
x=80

80 childrens tickets were sold.

To find the number of adults tickets sold, plug 80 into the first equation
x%2By=630
80%2By=630
y%2B80-80=630-80
y=550
550 adult tickets were sold.

to check if this is correct plug it into the second equation

2x%2B5y=2910
2%2880%29%2B5%28550%29=2910
160%2B2750=2910
2910=2910

80 childrens tickets and 550 adults tickets were sold.

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if you have any other questions, feel free to email me at ericahigley@yahoo.com