SOLUTION: Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 250 boxes. But when you raise your price to $4 you only sell 120 boxes. a. Write an equation f

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 250 boxes. But when you raise your price to $4 you only sell 120 boxes. a. Write an equation f      Log On

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Question 515003: Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 250 boxes. But when you raise your price to $4 you only sell 120 boxes.
a. Write an equation for the number of boxes you sell as a function of the price you charge.
b. Denote "B" for number of boxes, and "P" for the price you charge.
c. Assume the function is linear

Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!

B=-130P+640
the two points will be
P,B
3, 250
4, 120
slope will be 250-120/3-4
130/-1
-130
b=mp+y
120=-130*4+y
120=-520+y
120+520=y
640=y
b=-130p+640
check
250=-130*3+640
250=-390+640
250=640-390
250=250
ok
120=-130*4+640
120=640-520
120=120
ok

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let B = number of boxes
Let P = price charged
Assume a straight line
The data given tells what the slope of the line is.
Plot P on the vertical axis
Plot B on the horizontal axis
slope = +%284+-+3%29+%2F+%28+120+-+250+%29+
slope = +-1%2F130+
The equation so far is:
+P+=+-1%2F130%2AB+%2B+P%5B0%5D+
Where +P%5B0%5D+ is the vertical intercept
Plugging in data:
+-1%2F130+=+-.0077+
+3+=+-1%2F130%2A250+%2B+P%5B0%5D+
+P%5B0%5D+=+3+%2B+1.923+
+P%5B0%5D+=+4.923+
The equation is:
+P+=+-.0077B+%2B+4.923+
check answer:
+4+=+-.0077%2A120+%2B+4.923+
+4+=+-.924+%2B+4.923+
+4+=+3.999+ ( error due to rounding off)
and
+3+=+-.0077%2A250+%2B+4.923+
+3+=+-1.925+%2B+4.923+
+3+=+2.998+ ( also round-off error )
Here's the plot:
+graph%28+400%2C+400%2C+-50%2C+700%2C+-1%2C+6%2C+-.0077x+%2B+4.923+%29+