SOLUTION: The demand and supply equations for a certain item are given by D = –5p + 40 S = –p^2 + 30p – 8 Find the equilibrium price

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Question 104076: The demand and supply equations for a certain item are given by
D = –5p + 40
S = –p^2 + 30p – 8
Find the equilibrium price
Answer by elima(1433) About Me  (Show Source):
You can put this solution on YOUR website!
The demand and supply equations for a certain item are given by
D = –5p + 40
S = –p^2 + 30p – 8
Find the equilibrium price
Equilibrium is when supply = demand;
-5p%2B40=-p%5E2%2B30p-8
p%5E2-5p-30p%2B40%2B8=0
p%5E2-35p%2B48=0
Use quadratic equation to solve;
%2835%2B-sqrt%2835%5E2-4%281%29%2848%29%29%29%2F2%281%29
%2835%2B-sqrt%281225-192%29%29%2F2
%2835%2B-sqrt%281033%29%29%2F2
Now we two equations to solve, because we have 35+ and 35-;
P=%2835%2B32.14%29%2F2
P=33.57
P=%2835-32.14%29%2F2
P=2.86%2F2
P=1.43
:)