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 ->
Functions
-> 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 173563: 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.
My try at it:
1P = C50
2P = C25 Found 3 solutions by stanbon, Mathtut, josmiceli:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! 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.
---------
You have two points: (1,50) and (2,25)
slope = (25-50)/(2-1) = -25
-----------
Form: y = mx+b
intercept: 50 = -25*1 + b
b = 75
Equation:
C = -25p + 75
====================
Cheers,
Stan H.
You can put this solution on YOUR website! we have 2 points we will label then (P,C) (1,50) and (2,25) so lets find the slope....change in C over change in P
:
25-50/2-1=-25 which is the slope of our equation...now lets the point slope formula ...I am going to use point (2,25)
:
C-25=-25(P-2)
:
C-25=-25P+50
:
:
as you can see this can also be solved for P
:
divide all terms by -25
:
:
:
You can put this solution on YOUR website! The way to look at this is that you're graphing
price on the y-axis and cups on the x-axis.
Each point on the graph is (x,y) = (cups,price)
The problem gives you
(50,1) and
(25,2)
Since the problem says the relation is linear,
write the general equation for a straight line where
m = slope
b = y-intercept
Now plug in the given points one at a time
(1) and
(2)
Solve for and
Subtract (1) from (2)
Plug this back into (2)
So, the equation is answer
check the answer
Does it pass through the given points?
(50,1)
(25,2)
OK
If the price is the equation says I'll sell cups. I'd probably sell a lot more
When the price is $3, the equation says i'll sell
no cups because it's too expensive
(