Linear Equation Word Problem

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 $ 19, while 7000 shirts can be sold at a price of $ 13. Give a linear equation in the form p=mn+b that gives the price p they can charge for n shirts.

Answer 1

Okiedokie:

p = price

n = number of shirts

m = slope of the line   (note, the more shirts, the lower the price, so we know it's going to be negative)

b = y intercept

 

They are giving you 2 points here (5000, $19) and (7000, $13) which have to be on our line.

 

To find the slope m, you use m = (p1-p2)/(n1-n2)

Filling in from our points       m = (19-13)/(5000-7000)

                                          m = 6/-2000

                                          m = -.003

Now that we have the slope and a point, we can find our equation

p-p1=m(n-n1)

p-19=(-.003)(n-5000)

p-19= (-.003n) + 15

p=(-.003n) + 34

 

Then, just double check with the other point there: 

p=(-.003n) + 34

13 ? (-.003 x 7000) + 34

13 ? -21 + 34

13 = 13

 

Tada!