SOLUTION: 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 t

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Question 6936: 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.


Answer by glabow(165) About Me  (Show Source):
You can put this solution on YOUR website!
When P=1 then C=60.
When P=2 then C=30.
If you assume the function of P to C is linear, then you can calculate the change in C compared to the change in P.
This is called the slope of the line of an equation fitting these values.
%2860+-30%29%2F%281-2%29=30%2F-1=-30 is the slope.
This means that every time you increase P by 1, C will decrease by 30. That's the nature of a linear function.
The function of a line is y = ax + b, where a is the slope and b is the value of y when x=0 (called the y-intercept). In this case we are using C for y and P for x. The equation of the line is
C = -30P + b.
If the P were 0, what would C be? The slope tells us that every time you increase P by 1, C decreases by 30. Inversely, every time you decrease P by 1, C increases by 30. So when P=0, C=90.
The equation is
C = -30P + 90. (Not very realistic, but this fits the requirements of the problem.)