SOLUTION: adult tickets for a play cost $17 and child tickets cost $7. if there were 32 people at a performance and the theater collected $354 from ticket sales, how many adults and how man

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Question 106575: adult tickets for a play cost $17 and child tickets cost $7. if there were 32 people at a performance and the theater collected $354 from ticket sales, how many adults and how many children attended the play?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let A = the number of adults in attendance and C = the number of children in attendance.
A+C = 32 "...there were 32 people at a perfomance..."
A($17) + C($7) = $354 "...the theatre collected $354 from ticket sales,..."
So now we have two equtions with two unknowns (A and C):
A+C = 32 rewrite this as: C = 32-A
17A+7C = 354 Substitute the C = 32-A into this equation and solve for A.
17A + 7(32-A) = 354 Simplify.
17A + 224-7A = 354 After subtracting the A's, subtract 224 from both sides.
10A = 130 Divide both sides by 10.
A = 13 and...
C = 32-A
C = 32-13
C = 19
The number of adults attending = 13 and the number of children attending = 19