SOLUTION: When tickets for a rock concert cost $12, the average attendance was 500 people. Projections showed that for each $1 increase in ticket prices, 50 less people would attend. At what

Question 942527: When tickets for a rock concert cost $12, the average attendance was 500 people. Projections showed that for each $1 increase in ticket prices, 50 less people would attend. At what ticket price would the receipts be $5600
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
at:
$12 per ticket
500 people attend
(12,500)
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we're told that at:
12 + 1 = $13 per ticket
500 - 50 = 450 people attend
(13,450)
---
assume a linear relationship between ticket price and attendance:
---
slope = m
m = dy/dx
m = (500-450)/(12-13)
m = -50
---
the linear equation:
x = ticket price (dollars)
y = number of tickets sold
y - 500 = -50(x - 12)
y = -50x + 600 + 500
y = -50x + 1100
y = -50*8 + 1100
---
at what ticket price(s) would the receipts be $5600:
xy = 5600
x(-50x + 1100) = 5600
-50xx + 1100x - 5600 = 0
---
the above quadratic equation is in standard form, with a=-50, b=1100 and c=-5600
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-50 1100 -5600
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
---
the quadratic has two real roots at:
---
x = 8
x = 14
---
answer 1:
x = ticket price (dollars) = 8
y = number of tickets sold = -50*8 + 1100
y = number of tickets sold = 700
8*700 = 5600
---
answer 2:
x = ticket price (dollars) = 14
y = number of tickets sold = -50*14 + 1100
y = number of tickets sold = 400
14*400 = 5600
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