SOLUTION: A jazz group of tour has been drawing average crowds of 500 people. It is projected that for every $1.00 increase in the $12.00 ticket price, the average attendance will decrease b
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Question 211408This question is from textbook College Algebra
: A jazz group of tour has been drawing average crowds of 500 people. It is projected that for every $1.00 increase in the $12.00 ticket price, the average attendance will decrease by 50. At what ticket price will nightly recaipts be $5,600? Can you please get back to me before tues 10 am for that's when this is due. Please show me the steps
Thank you so much
This question is from textbook College Algebra
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
average crowd is 500 people when the ticket price is $12.00
Add $1.00 and the average number of people drops $50.00.
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r = x * y
where:
r = revenue
and:
x = number of people attending
and:
y = price per ticket
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you know that when x = 500 and y = 12, that r = 500*12 = 6000.
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you know that x is reduced by 50 when y is increased by 1.
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formula you would probably want to use to solve this would be:
$5600 = (500 - n*50) * (12 + n*1)
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n represents the number of times you would add 1 dollar to the price of the ticket, and it also represents the number of times you lose 50 people from attendance.
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solving this equation, you would simplify it by multiplying out the factors to get:
5600 = 6000 - 100n - 50n^2
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subtract 5600 from both sides of this equation to get:
0 = 400 - 100n - 50n^2
add 50n^2 and 100n to both sides of this equation and subtract 400 from both sides of this equation to get:
50n^2 + 100n - 400 = 0
divide both sides of this equation by 50 to get:
n^2 + 2n - 8 = 0
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factor this equation to get:
(n+4)*(n-2) = 0
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your answer is n = -4 or n = 2
since n can't be negative, your answer must be 2
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your original equation is:
$5600 = (500 - n*50) * (12 + n*1)
when n = 2, this becomes:
5600 = (500 - 2*50) * (12 + 2)
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This becomes:
5600 = 400 * 14
400 * 14 = 5600 confirming this answer is correct.
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