Precalc Question

Question

your friend Marvin makes and sells widgets as a hobby he believes he could sit a certain price that would maximizes profits and you agreed to help him with the math you tell Marvin to set the price at $2 per widget this next weekend and keep track of how many he sells and then the following weekend to set the price at $3 and keep track of how many he sells two weeks later he comes back to you and says when the price was $2 I sold 250 widgets but then when the price is $3 I only sold 175 below show Marvin how to write the number of widget sold as a function of price and write the price as a function of the number of widgets it sold

Answer 1

Let the price be p and the quantity q.

Assume a linear relationship between q and p: q=mp+a where m and a are constants.

So 250=2m+a when the price was $2 per widget and 175=3m+a when the price was $3.

Now, subtract one equation from the other:

75=-m, so m=-75. Therefore, 250=-150+a and a=400.

So the relationship is q=400-75p.