SOLUTION: A manufacturing company finds that they can sell 300 items if the price per item is $2.00, and $4.00 items if the price is $1.50 per item. If the relationship between the number of

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A manufacturing company finds that they can sell 300 items if the price per item is $2.00, and $4.00 items if the price is $1.50 per item. If the relationship between the number of      Log On


   

Question 1002682: A manufacturing company finds that they can sell 300 items if the price per item is $2.00, and $4.00 items if the price is $1.50 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. then use the formula to fund the number of items they will sell if the price per item is $3.00.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A manufacturing company finds that they can sell 300 items if the price per item is $2.00, and 400 items if the price is $1.50 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.
:
Find the slope using m = %28%28y2-y1%29%29%2F%28%28x2-x1%29%29, where
x1 = 2.00; y1=300
x2 = 1.50: y2=400
m = %28%28400-300%29%29%2F%28%281.5-2%29%29 = 100%2F%28-.5%29 = -200 is the slope
Point slope form to find the equation: y - y1 = m(x-x1)
y - 300 = -200(x - 2)
y - 300 = -200x + 400
y = -200x + 400 + 300
y = -200x + 700,
But they want to have x = items sold and p = the price, so we have to write
the equation where x is in terms of p
x = -200p + 700
:
then use the formula to find the number of items they will sell if the price per item is $3.00.
x = -200(3) + 700
x = -600 + 700
x = 100 items sold when the price is $3