SOLUTION: A jazz group on tour has been drawing average crowds of 600 people. It is projected that for every $1 increase in the $12 ticket price, the average attendance will decrease by 75.

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Question 838327: A jazz group on tour has been drawing average crowds of 600 people. It is projected that for every $1 increase in the $12 ticket price, the average attendance will decrease by 75. At what ticket price will nightly receipts be $6,300?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of $1 increases in ticket price:
+75n+ = the increase in attendance for +n+ $1
increases in ticket price
------------------------
+6300+=+%28+12+%2B+1%2An+%29%2A%28+600+-+75n+%29+
-----------------------------------
+6300+=+12%2A600+%2B+600n+-+12%2A75%2An+-+75n%5E2+
+75n%5E2+%2B+300n+-+900+=+0+
+n%5E2+%2B+4n+-+12+=+0+
+%28+n+-+2+%29%2A%28+n+%2B+6+%29+=+0+ ( I just guessed at this )
+n+=+2+ is the answer since +n+=+-6+ won't work
Plugging this back in:
+6300+=+%28+12+%2B+1%2An+%29%2A%28+600+-+75n+%29+
+6300+=+%28+12+%2B+1%2A2+%29%2A%28+600+-+75%2A2+%29+
+6300+=+14%2A450+
+6300+=+6300+
The nightly ticket price is +12+%2B+2+ = $14