SOLUTION: Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. Write an equation for

Algebra ->  Functions -> SOLUTION: Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. Write an equation for       Log On


   

Question 178908: Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 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 ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade
you sell 120 cups. But when you raise your price to $3 you only sell 60 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.
:
Make coordinates from the given information
x1=2, y1=120
x2=3, y2=60
:
Find the slope (m), where m = %28y2-y1%29%2F%28x2-x1%29:
m = %2860-120%29%2F%283-2%29
m = %28-60%29%2F1 = -60
:
write the equation using the point/slope formula [y-y1 = m(x-x1)]
y - 120 = -60(x - 2)
y - 120 = -60x + 120
y = -60x +120 + 120
y = -60x + 240
Translate this to your problem where x=p, y=C
C(p) = -60p + 240
:
:
you can check this by substituting 2 for p and ensuring that C(p) = 120
do the same for p=3