SOLUTION: A band has been drawing average crowds of 500 people. It is thought that for every $1 increase in the $12 ticket price, the average attendence will decrease by 50. At what ticket

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Question 129531: A band has been drawing average crowds of 500 people. It is thought that for every $1 increase in the $12 ticket price, the average attendence will decrease by 50. At what ticket price will the nightly receipts be $5600?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the number of $1 ticket increases
12+%2B+n is the ticket price
50n is the decrease in attendence for each $1
increase in ticket price
500+-+50n is the attendence for each $1
increase in ticket price
%28500+-+50n%29%2812+%2B+n%29+=+5600
6000+-+600n+%2B+500n+-+50n%5E2+=+5600
subtract 5600 from both sides
400+-+600n+%2B+500n+-+50n%5E2+=+0
Multiply both sides by -1
-400+%2B+600n+-+500n+%2B+50n%5E2+=+0
50n%5E2+%2B+100n+-+400+=+0
divide both sides by 50
n%5E2+%2B+2n+-+8+=+0
%28n+%2B+4%29%28n+-+2%29
n+=+-4
n+=+2
12+%2B+n is the ticket price
The nightly receipts are $5600 when the ticket
price is $14
check answer:
%28500+-+50n%29%2812+%2B+n%29+=+5600
500+-+50%2A2%29%2812+%2B+2%29+=+5600
400%2A14+=+5600
5600+=+5600
OK