SOLUTION: Adult tickets for a play cost $9 and child tickets cost $3. If there were 24 people at a performance and the theater collected $186 from ticket sales, how many children attended?

Question 165451: Adult tickets for a play cost $9 and child tickets cost $3. If there were 24 people at a performance and the theater collected $186 from ticket sales, how many children attended?
Found 2 solutions by stanbon, Mathtut:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Adult tickets for a play cost $9 and child tickets cost $3. If there were 24 people at a performance and the theater collected $186 from ticket sales, how many children attended?
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EQUATION:
value + value = 186
9a + 3(24-a) = 186
9a + 72 - 3a = 186
6a = 114
a = 19 (# of adult tickets sold)
24-19 = 5 (# of child tickets sold)
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Cheers
Stan H.
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
let Adult =A and child=C we have A+C=24 and we also know that 9times A+3 times C=186 or 9A+3C=186. Now taking the first equation rewriting it to C=24-A and then substituting the value of A into the 2nd equation we get
9A+3(24-A)=186 distributing the 2nd term we get 9A+72-3A=186 which simplifies to 6A=114 divide by 6 and A=19 C=24-A(19)=5
answer # of children is 5
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