SOLUTION: Please help me solve this equation: Last year the promoter of an outdoor music festival charged patrons $45 and had a total attendance of 12 500 people. This year the promoter char

Question 344475: Please help me solve this equation: Last year the promoter of an outdoor music festival charged patrons $45 and had a total attendance of 12 500 people. This year the promoter charged $50 and had a total attendance of 10 900 people.
(a) Assuming there is a linear relationship between the number N of people attending and the price P of the ticket, find the linear equation relating N and P.
(b) If the promoter were to price the tickets at $35 next year, how many people would be expected to attend?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Last year the promoter of an outdoor music festival charged patrons $45 and had a total attendance of 12 500 people. This year the promoter charged $50 and had a total attendance of 10 900 people.
(a) Assuming there is a linear relationship between the number N of people attending and the price P of the ticket, find the linear equation relating N and P.
---
You have two points that relate attendance to price:
(45,12,500) and (50,10,900)
slope = (10900-12500)/(50-45) = -1600/5 = -320
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Form: N = mp + b
10,900 = -320*50 + b
b = 10,900+16000
b = 26,900
---------------------
Equation:
N(p) = -320p + 26,900
=========================
(b) If the promoter were to price the tickets at $35 next year, how many people would be expected to attend?
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N(35) = -320*35+26,900
N(35) = 15,700
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Cheers,
Stan H.
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