6. Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 100 cups. But when you raise your price to $4 you only sell 50 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.

Question

6. Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 100 cups. But when you raise your price to $4 you only sell 50 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 1

From the data, C*P=200

C= 200/P

One can assume all one wants, but the funcion is not linear.

Answer 2

To find the equation for the number of cups you sell as a function of the price you charge, we need to determine the equation of a straight line that passes through two given points: (100, 2) and (50, 4).

We can use the slope-intercept form of a linear equation, which is given by:

y = mx + b

where y is the dependent variable (number of cups), x is the independent variable (price), m is the slope, and b is the y-intercept.

To find the slope (m), we can use the formula:

m = (y2 - y1) / (x2 - x1)

Using the points (100, 2) and (50, 4):

m = (4 - 2) / (50 - 100)
= 2 / (-50)
= -0.04

Now, we can substitute one of the points and the slope into the slope-intercept form to find the y-intercept (b).

Using the point (100, 2):

2 = (-0.04)(100) + b

2 = -4 + b

b = 2 + 4
= 6

Therefore, the equation for the number of cups you sell (C) as a function of the price you charge (P) is:

C = -0.04P + 6

Answer 3

To write the equation for the number of cups you sell as a function of the price you charge, we can use the formula for a line in slope-intercept form: y = mx + b.

In this case, let "C" represent the number of cups sold and "P" represent the price charged. We are given two points on the line: (100, 2) and (50, 4).

First, we need to find the slope (m) of the line. The slope is calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Using the given points: (100, 2) and (50, 4):

Substituting the values:

m = (4 - 2) / (50 - 100)

Simplifying:

m = 2 / (-50)

m = -0.04

Next, we need to find the y-intercept (b) of the line. We can use the slope-intercept form of the line equation and substitute one of the given points:

y = mx + b

2 = (-0.04)(100) + b

Simplifying:

2 = -4 + b

b = 6

Therefore, the equation for the number of cups sold as a function of the price charged is:

C = -0.04P + 6