SOLUTION: Adult tickets for a play cost $20 and child tickets cost $5. If there were 31 people at the performance, and the theater collected $416.00 from ticket sales, how many children atte

Algebra ->  Equations -> SOLUTION: Adult tickets for a play cost $20 and child tickets cost $5. If there were 31 people at the performance, and the theater collected $416.00 from ticket sales, how many children atte      Log On


   

Question 117114: Adult tickets for a play cost $20 and child tickets cost $5. If there were 31 people at the performance, and the theater collected $416.00 from ticket sales, how many children attended?
a.11
b.12
c.13
d.19
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
a = number of adults
c = number of children
20a+%2B+5c+=+416
a+%2B+c+=+31
a+=+31+-+c
20%2831+-+c%29+%2B+5c+=+416
620+-+20c+%2B+5c+=+416
15c+=+620+-+416
15c+=+204
c+=+13.6
The closest answer is c. 13
If the answer is 13 children, and a+%2B+c+=+31
a+=+31+-+13
a+=+18 and
20a+%2B+5c+=+416
20%2A18+%2B+5%2A13+=+416
360+%2B+65+=+416
425+=+416 obviously not true
So, they either miscounted their receipts, undercharged somebody,
or $9 got lost or stolen!!! But c. is still closest answer