Question 849517: A manufacturing company finds that they can sell 300 items at $2.00 per item and 175 items at $2.50 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=_____
Now use the formula to find the number of items they will sell if the price per item is $1.50.
They will sell___items if the price is $1.50.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! y = number of items sold.
x = price per item.
when x = 2, y = 300
when x = 2.5, y = 175
(x1,y1) = (2,300)
(x2,y2) = (2.5,175)
slope = (y2-y1) / (x2-x1) = (175-300) / (2.5-2) = -125 / .5 = -250
point slope form of equation of a straight line is y-y1 = m(x-x1)
m is equal to -250
let x1 = 2 and y1 = 300
equation becomes:
y-300 = -250(x-2)
simplify to get:
y-300 = -250x + 500
add 300 to both sides of this equation to get:
y = -250x + 800
that's your equation.
y = -250x + 800
when x = 1.5, this equation becomes:
y = -250(1.5) + 800 which becomes:
y = -375 + 800 which becomes:
y = 425
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