Question

A clothing business finds there is a linear relationship between the number of shirts, n ,it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 5000 shirts can be sold at a price of $ 57 , while 15000 shirts can be sold at a price of $ 7 . Give a linear equation in the form p = m n + b that gives the price p they can charge for n shirts.

Answer 1

p = -0.005n + 82

Answer 2

The equation that gives the price p they can charge for n shirts is

p = -0.005n + 82

Step-by-step explanation:

Establish the variables for the equation

n = number of shirts that can sell

p = price per shirt

For case one we have n1 = 5000 p1 =$57

For case two we have n2 = 15000 p2= $7

Calculate the slope remeber that
`m=(y2-y1)/(x2-x1)` in this case the y will be represented by the price (p) and the x by the number (n) so we have:

m =
`m= (p2-p1)/(n2-n1) = (7-57)/(15000-5000) = (-50)/(10000)=   (-5)/(1000) =-0.005`

Replace in the equation (y-y1) = m (x - x1) with our variables:

(p-p1) = m(n-n1)

p - 57 = -0.005 (n - 5000)

p - 57 = -0.005n + 25

p = -0.005n + 25 + 57

p = -0.005n + 82

To verify we can replace for example the values of n2 to get p2 as follows

p= -0.005 (15000) + 82

p = - 75 + 82

p = 7

If fulfills the condition that for 15000 shirts the price is $ then the equation is correct