SOLUTION: The demand equation for a certain type of printer is given by D=-200p + 35,000. The supply equation is predicted to be S=-p^2+400p-20,000. My answer is: D=S -200p+

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Question 88618: The demand equation for a certain type of printer is given by D=-200p + 35,000. The supply equation is predicted to be S=-p^2+400p-20,000.
My answer is: D=S
-200p+35000=p^2+400p-20000
p^2-600p+55000=0
Whereas p^2+ap+b=0, Am I right??? Thanks ;0)
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
I'm assuming you're looking for the equilibrium price right?

To find the equilibrium price, set D equal to S


Subtract from both sides

Subtract from both sides

Add to both sides

Combine like terms



Now let's use the quadratic formula to solve for p:


Starting with the general quadratic



the general solution using the quadratic equation is:



So lets solve ( notice , , and )

Plug in a=-1, b=-600, and c=55000



Negate -600 to get 600



Square -600 to get 360000



Multiply to get



Combine like terms in the radicand (everything under the square root)



Simplify the square root



Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

or

that simplify to

or


Which approximate to

or


So our possible solutions are:
or


Since a negative price doesn't make sense, we must discard the negative solution

So the equilibrium price is $80.79
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