SOLUTION: 15. Adult tickets for a play cost $16 and child tickets cost $9. If there were 24 people at a performance and the theater collected $258 from ticket sales, how many children atten

Algebra ->  Expressions-with-variables -> SOLUTION: 15. Adult tickets for a play cost $16 and child tickets cost $9. If there were 24 people at a performance and the theater collected $258 from ticket sales, how many children atten      Log On


   

Question 39394: 15. Adult tickets for a play cost $16 and child tickets cost $9. If there were 24 people at a performance and the theater collected $258 from ticket sales, how many children attended the play?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A = number of adults
C = number of children
A + C = 24
solve for A
(a)A = 24 - C
(b)258 = 16A + 9C
(price per adult ticket) X (number of tickets) = amount collected from adults
(price per child ticket) X (number of tickets) = amount collected from children
substitute (a) in (b)
258 = 16(24 - C) + 9C
258 = 16*24 - 16C + 9C
258 = 384 - 7C
subtract 384 from both sides
-126 = -7C
multiply both sides by -1
7C = 126
C = 18
(a)A = 24 - C
A = 24 - 18
A = 6
check:
(b)258 = 16A + 9C
258 = 16*6 + 9*18
258 = 96 + 162
258 = 258
OK
18 children attended the play