SOLUTION: 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 wi

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Question 30720: 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?
Found 2 solutions by Paul, AnlytcPhil:
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the number of $1 increase:

Cost of tickets: x+12

Tickets sold = 500-50x

Equation:

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







Multiply the whole equation by -1 to remove the negative and simplfy:





Use the quadratic formula:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

a=1, b=2, c=-8

x=%28-2%2B-sqrt%282%5E2-4%2A1%2A-8%29%29%2F%282%2A1%29

x=%28-2%2B-sqrt%2836%29%29%2F2

x=%28-2-6%29%2F2 or x=%28-2%2B6%29%2F2

Remove the negative: and simplfy to get:

x=2



12+2=14

Hence, it will be $14.

Paul.

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
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?

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