Question 30720
<pre><b>Please help me!!! A jazz group on tour has been drawing average crowds of 500
persons. It is projected that for every $1 increase in the $12 ticket price,
the average attendance will decrease by 50. At what ticket price will the
nightly receipts be $5600?
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Let x = the number of $1 increases in price

Let y = the nightly receipts

Then the price per ticket will be $(12 + x)

and so the number attending will be 500 - 50x

Nightly receipt = (Price per ticket)×(the number of attendees) =

              y = (12 + x)(500 - 50x)

So we substitute 5600 for y.

            5600 = (12 + x)(500 - 50x)

Can you solve this? If not post again. 

There are two solutions, x = -4 and x = 2

Choose the positive answer, discard the negative one.

Check:

When there are 2 $1 tickets the price per ticket is $14 
There were 500 - 2(50) = 400 attendees.
The intake is $14 times 400 or $5600

Edwin
AnlytcPhil@aol.com</pre>