Question 5887: Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 60 cups. But when you raise your price to $2 you only sell 30 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear.
I know this may seem really easy, but I have been looking at it forever and I can't figure it out. I want to help my cousin with his homework but it's above my head. Thanks for all your help.
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! when P=1 --> C=60
when P=2 --> C=30
imagine a grpah of C against P...just like y-against-x.
We have 2 coordinates (1, 60) and (2, 30). Now, assuming it is linear, we can find the gradient, m from:
m = 
m = (60-30)/(1-2)
m = 30/-1
m = -30
so, from the general equation of a straight line, y=mx+c, we now know that y=-30x+c. Now for c. To find this, we need to know both "x" and "y"...which we do: we have 2 sets of points. So pick one of them..i chose (1,60):
60 = -30(1) + c
60 = -30 + c
c = 90
so, equation is now C = -30P + 90
jon.
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