SOLUTION: A jazz group on tour has been drawing average crowds of 400 people. It is projected that for every $1 increase in the $15 ticket price, the average attendance will decrease by 50.

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Question 945398: A jazz group on tour has been drawing average crowds of 400 people. It is projected that for every $1 increase in the $15 ticket price, the average attendance will decrease by 50. At what ticket price will nightly receipts be $3,000?

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
+15+%2B+n%2A1+ = projected ticket price
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+%28+15+%2B+n+%29%2A%28+400+-+50n+%29+=+3000+
+6000+%2B+400n+-+750n+-+50n%5E2+=+3000+
+50n%5E2+%2B+350n+-+3000+=+0+
+n%5E2+%2B+7n+-+60+=+0+
+%28+n+%2B+12+%29%2A%28+n+-+5+%29+=+0+ ( by looking at it )
+n+=+5+ ( result must be positive )
-----------------
+15+%2B+n%2A1+ = projected ticket price
+15+%2B+5+=+20+
At a ticket price of $20, receipts will be $3,000
check:
+%28+15+%2B+n+%29%2A%28+400+-+50n+%29+=+3000+
+%28+15+%2B+5+%29%2A%28+400+-+50%2A5+%29+=+3000+
+20%2A%28+400+-+250+%29+=+3000+
+20%2A150+=+3000+
+3000+=+3000+
OK