SOLUTION: Adult tickets for a play cost $11 and child tickets cost $10. If there were 23 people at a performance and the theater collected $246 from ticket sales, how many children attended

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Question 54709: Adult tickets for a play cost $11 and child tickets cost $10. If there were 23 people at a performance and the theater collected $246 from ticket sales, how many children attended the play?
Found 2 solutions by checkley71, tutorcecilia:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
A+C=23
11A+10C=246
A=23-C
11(23-C)+10C=246
253-11C+10C=246
-C=246-253
-C=-7
C=7
THEN A+7=23
A=23-7
A=16
PROOF
11*16+10*7=246
176+70=246
246=246

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
Ax+By=C [Use the standard equation of a line]
x+y=23 [Total tickets sold, so substitute (y=23-x)]
($10)(x)+($11)(23-x)=$246
10x+11(23-x)=246
10x+253-11x=246
10x-11x=246-253
-1x=-7
x=7
.
So,
Children's tickets=($10)(7)=$70
Adult's tickets = ($11)(23-7)=$176
$176+$70=$246