SOLUTION: Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 50 cups. But when you raise your price to $2 you only sell 25 cups. Write an equation for t

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 50 cups. But when you raise your price to $2 you only sell 25 cups. Write an equation for t      Log On


   



Question 198209: Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 50 cups. But when you raise your price to $2 you only sell 25 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.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If I plot price on the vertical axis and # of cups
on the horizontal axis, I have 2 points given:
(50,1) and (25,2)
The formula to use is:
%28P+-+2%29+%2F+%28C+-+25%29+=+%281+-+2%29+%2F+%2850+-+25%29
%28P+-+2%29+%2F+%28C+-+25%29+=+-1+%2F+25
Multiply both sides by 25%2A%28C+-+25%29
25%2A%28P+-+2%29+=+-1%2A%28C+-+25%29
25P+-+50+=+-C+%2B+25
25P+=+-C+%2B+75
P+=+%28-1%2F25%29%2AC+%2B+3 answer
check:
does the line go through (50,1) and (25,2)?
25P+=+-C+%2B+75
25%2A1+=+-50+%2B+75
25+=+25
OK
25P+=+-C+%2B+75
25%2A2+=+-25+%2B+75
50+=+50
OK
Here's the plot:
+graph%28+400%2C+400%2C+-10%2C+100%2C+-1%2C+6%2C+-x%2F25+%2B+3%29