Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 200 boxes. But when you raise your price to $4 you only sell 120 boxes. Write the equation for the number of boxes you sell as a function of the price you charge. Denote "b" for the number of boxes, and "p" for prices you charge, assume the function is linear.
b = k p + c where k and c are constants
200 = k (3) + c
120 = k (4) + c
------------------subtract
80 = -1 k
so
k = -80
back to first eqn
200 = -80(3) + c
200 = -240 + c
c = 440
so
b = -80 p + 440
Thank you, I was stuck on this for several hours to how to write this out, thank you again!
To write the equation for the number of boxes sold as a function of the price charged, we can use the concept of a linear equation. A linear equation has the general form: b = m * p + c, where "b" represents the number of boxes sold, "p" represents the price charged, "m" represents the slope (rate of change), and "c" represents the y-intercept (the value of "b" when "p" is zero).
To find the values of "m" and "c," we can use the information given in the problem:
When the price is $3 (p = 3), 200 boxes are sold (b = 200).
When the price is $4 (p = 4), 120 boxes are sold (b = 120).
Using these two data points, we can calculate the slope "m" using the formula:
m = (change in b) / (change in p) = (120 - 200) / (4 - 3) = -80.
Now, we can substitute one set of values (p, b) into the linear equation and solve for "c." Let's use the data point (3, 200):
200 = -80 * 3 + c
200 = -240 + c
c = 200 + 240
c = 440
Therefore, the equation for the number of boxes sold (b) as a function of the price charged (p) can be expressed as:
b = -80p + 440