Question 326778
The equilibrium price and quantity occurs when the demand equals the supply.  At equilibrium, both demand and supply have the same price and same quantity.  So since both equations have the same value for P at equilibrium, and both equations equal P, you can set them equal to each other:
-0.5Q + 30.95 = P = 0.3Q + 2.15
Now solve for Q by combining like terms:
-0.5Q + 30.95 = 0.3Q + 2.15   (now subtract 2.15 from each side)
-0.5Q + 28.8 = 0.3Q   (now add 0.5Q to each side)
28.8 = 0.8Q   (now divided each side by 0.8)
36 = Q
So your equilibrium quantity is 36.  Now plug this into either the demand or the supply equations to find P.  Using either equation will get you the same answer - I am just choosing to use the demand equation.
P = -0.5Q + 30.95
P = -0.5(36) + 30.95
P = -18 + 30.95
P = 12.95
So the equilibrium price is $12.95.