SOLUTION: I have got NO idea where to start on this one: Any and all help is MUCHO appreciated, thanks! A manufacturing company finds that they can sell 275 items at $2.50 per item and 35

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I have got NO idea where to start on this one: Any and all help is MUCHO appreciated, thanks! A manufacturing company finds that they can sell 275 items at $2.50 per item and 35      Log On


   



Question 725935: I have got NO idea where to start on this one: Any and all help is MUCHO appreciated, thanks!
A manufacturing company finds that they can sell 275 items at $2.50 per item and 350 items at $2.00 per item. If the relationship between the number of items sold x and the price per item p is a linear one:
Find a formula that gives x in terms of p: x=_______

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We are used to writing y as a function of x.
In this case, you need to write x as a (linear) function of p,
x=mp%2Bb instead of y=mx%2Bb
It is a linear function, so it graphs as a straight line.
That line passes through the points
(2.50,275), with coordinates p=2.50 and x=275, and
(2.00,350), with coordinates p=2.00 and x=350

To graph that line we have to change the labels on the axes to read p and x, instead of x and y

To write the equation we can find the slope of the line passing through points (2.50,275) and (2.00,350) :
m=%28275-350%29%2F%282.5-2%29=-75%2F2.5=-150
write the line in point slope form using point (2.350) as
x-350=-150%28p-2%29
and do a little algebra to transform that into the slope-intercept form
(or "solve for x").
x-350=-150%28p-2%29 --> x-350=-150p%2B300%29 --> highlight%28x=-150p%2B650%29%29