SOLUTION: Adult tickets for a play cost $11.00 and child tickets cost $10.00. If there were 23 people at a performance and the theater collected $246.00 from ticket sales, how many children

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Question 69084: Adult tickets for a play cost $11.00 and child tickets cost $10.00. If there were 23 people at a performance and the theater collected $246.00 from ticket sales, how many children attended the play?
Please help me to solve this
Found 2 solutions by Nate, jim_thompson5910:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
a = number of adult tickets
c = number of child tickets
a + c = 23 or a = 23 - c
11a + 10c = 246
Plug:
11(23 - c) + 10c = 246
253 - 11c + 10c = 246
-c = -7
c = 7
a = 23 - 7 = 16
16 adult tickets and 7 child tickets

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Let a=adults, c=children
11a%2B10c=246money made from adult's and children's tickets
a%2Bc=23 number of people
a=23-c solve for any variable, in this case a
11%2Ahighlight%28%2823-c%29%29%2B10c=246plug in value of a in terms of c
253-11c%2B10c=246Distribute
253-c=246Simplify
-c=-7Isolate c
c=7Negate to make c a positive number
So the number of children that attended is 7
a%2Bhighlight%287%29=23Plug in number of children and solve for number of adults
a=16
So there were 16 adults and 7 children