Question 211408
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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