Question

Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 250 boxes. But when you raise your price to $4 you only sell 120 boxes.

a. Write an equation for the number of boxes you sell as a function of the price you charge.

b. Denote "B" for number of boxes, and "P" for the price you charge.

c. Assume the function is linear..

Answer 1

Look at it as if you are given two ordered pairs
(3,250) and (4,120) of the form (P,B)
slope = (120-25)/(4-3) = -130/1 = -130

then just like in y = mx + b
B = -130P + b
sub in (4,120)
120 = -130(4) + b
b = 640

<b>B = -130P + 640</b>

check:
if P= 3 , B = -130(3) + 640 = 250
if P = 4 , B = -130(4) + 640 = 120

All is good.