Math

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

  • Math -

    c = m p + b
    50 = m (1) + b
    25 = m(2) + b
    ------------- subtract
    25 = - m
    m = -25 the slope
    then
    25 = -25 (2) + b
    75 = b the intercept with cup axis
    so
    c = -25 p + 75

    so if I charged nothing, I would give away 75 cups
    and if I charged three, I would sell none :)

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