SOLUTION: I am having problems with this word problem. The demand and supp;y equations for a certain item are given by D=-5p+40 S=-p^2+30-8 find the equilibrium price. Thanks a

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am having problems with this word problem. The demand and supp;y equations for a certain item are given by D=-5p+40 S=-p^2+30-8 find the equilibrium price. Thanks a       Log On


   

Question 92925: I am having problems with this word problem.

The demand and supp;y equations for a certain item are given by
D=-5p+40
S=-p^2+30-8
find the equilibrium price.
Thanks a million
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equilibrium price, p, for the Demand and Supply equations:
D+=+-5p%2B40
S+=+-p%5E2%2B30p-8 I assume that you had a typo in your post because you had written:S+=+-p%5E2%2B30-8
The equilibrium occurs when demand, D, equals supply, S.
-5p%2B40+=+-p%5E2%2B30p-8 Let's put this into a standard-form quadratic equation:
ax%5E2%2Bbx%2Bc+=+0.
p%5E2-35p%2B48+=+0 Solve using the quadratic formula:p+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
p+=+%28-%28-35%29%2B-sqrt%28%28-35%29%5E2-4%281%29%2848%29%29%29%2F2%281%29
p+=+%2835%2B-sqrt%281225-192%29%29%2F2
p+=+%2835%2B-sqrt%281033%29%29%2F2
p+=+%2835%2B32.14%29%2F2 or p+=+%2835-32.14%29%2F2
The final answer is that there are two equilibrium prices:
p = $33.57 or p = $1.43