I need help solving an equilibrium point problem, how do I even write out this equation?

Question

A company makes hammers and for $20, they will make 90 hammers.  Consumers will only buy 73 of them. If the company lowers the price to $14, consumers will purchase 94 hammers, but the company would only make 60 of them. What is the equilibrium price and quantity of hammers that should be made? 

Answer 1

demand is downward sloping: P=-(2/7)Q +283/7 where P=price and Q= quantity of output

(73,20), (94,14) are points on the demand line

supply is upward sloping P=(1/5)Q + 2, (60,14) and (90,20) are points on the supply line

set them equal and solve for Q = about 79.12 at equilibrium output

substitute that into either equation and solve for P = about $17.82 for equilibrium price

plot the points and lines graphically. You can see equilibrium is between 14 and 20 for price

and between 73 and 90 for output. midway is about 17 and 81, an approximation, which is close