SOLUTION: 10. 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 at

Algebra ->  Equations -> SOLUTION: 10. 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 at      Log On


   

Question 43724: 10.
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?



A) 8 children B) 16 children C) 7 children D) 6 children
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
Number of adults = a
Number of children = c
a+%2B+c+=+23
11a+%2B+10c+=+246
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Ca+%2B+1%5Cc+=+23%2C%0D%0A++++11%5Ca+%2B+10%5Cc+=+246+%29%0D%0A++We'll use substitution. After moving 1*c to the right, we get:
1%2Aa+=+23+-+1%2Ac, or a+=+23%2F1+-+1%2Ac%2F1. Substitute that
into another equation:
11%2A%2823%2F1+-+1%2Ac%2F1%29+%2B+10%5Cc+=+246 and simplify: So, we know that c=7. Since a+=+23%2F1+-+1%2Ac%2F1, a=16.

Answer: system%28+a=16%2C+c=7+%29.