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) About Me  (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
-200p%2B35000=p%5E2%2B400p-20000

-200p%2B35000-p%5E2=400p-20000Subtract p%5E2 from both sides

-200p%2B35000-p%5E2-400p=-20000Subtract 400p from both sides

-200p%2B35000-p%5E2-400p%2B20000=0 Add 20000 to both sides

-p%5E2-600p%2B55000=0 Combine like terms



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


Starting with the general quadratic

ap%5E2%2Bbp%2Bc=0

the general solution using the quadratic equation is:

p+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve -p%5E2-600%2Ap%2B55000=0 ( notice a=-1, b=-600, and c=55000)

p+=+%28--600+%2B-+sqrt%28+%28-600%29%5E2-4%2A-1%2A55000+%29%29%2F%282%2A-1%29 Plug in a=-1, b=-600, and c=55000



p+=+%28600+%2B-+sqrt%28+%28-600%29%5E2-4%2A-1%2A55000+%29%29%2F%282%2A-1%29 Negate -600 to get 600



p+=+%28600+%2B-+sqrt%28+360000-4%2A-1%2A55000+%29%29%2F%282%2A-1%29 Square -600 to get 360000



p+=+%28600+%2B-+sqrt%28+360000%2B220000+%29%29%2F%282%2A-1%29 Multiply -4%2A55000%2A-1 to get 220000



p+=+%28600+%2B-+sqrt%28+580000+%29%29%2F%282%2A-1%29 Combine like terms in the radicand (everything under the square root)



p+=+%28600+%2B-+100%2Asqrt%2858%29%29%2F%282%2A-1%29 Simplify the square root



p+=+%28600+%2B-+100%2Asqrt%2858%29%29%2F-2 Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

p+=+%28600+%2B+100%2Asqrt%2858%29%29%2F-2 or p+=+%28600+-+100%2Asqrt%2858%29%29%2F-2

that simplify to

p+=+-300+-50%2Asqrt%2858%29 or p+=+-300+%2B+50%2Asqrt%2858%29


Which approximate to

p=-680.788655293195 or p=80.7886552931954


So our possible solutions are:
p=-680.788655293195 or p=80.7886552931954


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

So the equilibrium price is $80.79