SOLUTION: A jazz group on tour has been drawing average crowds of 600 people. It is projected that for every $1 increase in the $11 ticket price, the average attendance will decrease by 75.

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Question 990268: A jazz group on tour has been drawing average crowds of 600 people. It is projected that for every $1 increase in the $11 ticket price, the average attendance will decrease by 75. At what ticket price will nightly receipts be $3,600?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of $1 increases in ticket price
+3600+=+%28+600+-+75n+%29%2A%28+11+%2B+1%2An+%29+
+3600+=++6600+-+825n+%2B+600n+-+75n%5E2+
+-75n%5E2+-+225n+%2B+3000+=+0+
+-n%5E2+-+3n+%2B+40+=+0+
+n%5E2+%2B+3n+-+40+=+0+
I notice +8%2A%28-5%29+=+-40+ and
+8+-+5+=+3+, so
+%28+n+%2B+8+%29%2A%28+n+-+5+%29+=+0+
+n+=+5+ ( can't use the negative root )
and
+11+%2B+1%2An+=+11+%2B+1%2A5+
+11+%2B+1%2An+=+16+
At $16 ticket price receipts are $3,600
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check:
+3600+=+%28+600+-+75n+%29%2A%28+11+%2B+1%2An+%29+
+3600+=+%28+600+-+75%2A5+%29%2A%28+11+%2B+1%2A5+%29+
+3600+=+%28+600+-+375+%29%2A16+
+3600+=+225%2A16+
+3600+=+3600+
OK