SOLUTION: Hi: I have this word problem that I'm uncertain how to set up to solve. If someone could give me directions, I'd be grateful. Cheers! Angela Problem: "daily demand for a cer

Algebra ->  Equations -> SOLUTION: Hi: I have this word problem that I'm uncertain how to set up to solve. If someone could give me directions, I'd be grateful. Cheers! Angela Problem: "daily demand for a cer      Log On


   

Question 589959: Hi: I have this word problem that I'm uncertain how to set up to solve. If someone could give me directions, I'd be grateful. Cheers! Angela
Problem:
"daily demand for a certain item is 500/p, where p is the price of the item in dollars. The daily supply is 2p-1. At what price does supply equal demand?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
daily demand for a certain item is 500/p, where p is the price of the item in dollars. The daily supply is 2p-1.
At what price does supply equal demand?
:
They asking at what p, is the supply = to the demand, therefore
2p - 1 = 500%2FP
multiply both sides by p
2p^2 - p = 500
2p^2 - p - 500 = 0; a quadratic equation, use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem x=p; a=2; b=-1; c=-500
p+=+%28-%28-1%29+%2B-+sqrt%28-1%5E2-4%2A2%2A-500+%29%29%2F%282%2A2%29+
p+=+%281+%2B-+sqrt%281+%2B+4000+%29%29%2F4+
p+=+%281+%2B-+sqrt%284001+%29%29%2F4+
We only care about the positive solution here
p+=+%281+%2B+63.253%29%2F4+
p = 64.253%2F4
p = $16.06 is the price for equal supply and demand
:
:
see if that checks out in each equation
2(16.06) - 1 = 31.12
500%2F16.06 = 31.13, close enough