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**need help finishing problem!!**

For a certain commodity, the deman equation is given by D= -5p + 50. At a price of $1, twelve units of the commodity are supplied. If the supply equation is linear and the market price is $4, find the supply equation.

I know that the supply equation is linear, it must be of the form

s= ap+ b. I also know that "At a price of $1, twelve units of the commodity are supplied"- that is, when p= 1, s= 12 so 12= a(1)+ b or a+ b= 1. That means that b= 1- a and the supply equation can be written s= ap+ 1- a. Finally, its says that the "Market price is $4" which means that the value of p at which the supply and demand equations give s= D is 4. The demand equation is D= -5p + 5. When p= 4, what is D? I know what D equals. I also know s: s= D. I'm just not sure how put that value of s as well as p= 4 into the supply equation and solve for a. Can someone help!

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