SOLUTION: Please help me with this. Detailed workings are very much appreciated, thanks! The weekly demand and supply functions for a type of watch is given by p=-0.1x^2-x+40 and p=0.1x^

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Question 1045240: Please help me with this. Detailed workings are very much appreciated, thanks!
The weekly demand and supply functions for a type of watch is given by
p=-0.1x^2-x+40 and p=0.1x^2+2x+20 respectively,
where p is measured in dollars and x is measured in units of a hundred. Find the equilibrium quantity and price.
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
set the two equal to each other, for then it is in equilibrium.
-0.1x^2-x+40 =0.1x^2+2x+20, put everything on the right.
0=0.2x^2+3x-20
multiply everything by 5 to make the x^2 leading coefficient 1.
0=x^2+15x-100
0=(x+20)(x-5)
x=5, since x can't equal -20
That is 500 watches since x is hundreds.
now substitute into both, since they should be the same to check
-2.5-5+40=$32.50
2.5+10+20=$32.50
That is 500 watches at $32.50 each for the equilibrium price.

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

Please help me with this. Detailed workings are very much appreciated, thanks!
The weekly demand and supply functions for a type of watch is given by
p=-0.1x^2-x+40 and p=0.1x^2+2x+20 respectively,
where p is measured in dollars and x is measured in units of a hundred. Find the equilibrium quantity and price.

Equilibrium quantity (x) and equilibrium price (p) occur when demand equals supply.
We then equate the demand and supply functions, to get:

------ Multiplying equation by 5 to get rid of the decimal
(x - 5)(x + 20) = 0
x, or equilibrium quantity =
------- Substituting 5 for x in demand function (could've also substituted 5 in the supply function)
p = - 0.1(25) - 5 + 40
p = - 2.5 - 5 + 40
p, or equilibrium price =