Question

Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 200 boxes. But when you raise your price to $4 you only sell 120 boxes. Write the equation for the number of boxes you sell as a function of the price you charge. Denote "b" for the number of boxes, and "p" for prices you charge, assume the function is linear.

Answer 1

b = k p + c where k and c are constants
200 = k (3) + c
120 = k (4) + c
------------------subtract
80 = -1 k
so
k = -80
back to first eqn
200 = -80(3) + c
200 = -240 + c
c = 440
so
b = -80 p + 440

Answer 2

Thank you, I was stuck on this for several hours to how to write this out, thank you again!