Linear Equations Word Problem

Question

A clothing business finds there is a linear relationship between the number of shirts,,it can sell and the price,, it can charge per shirt. In particular, historical data shows that  shirts can be sold at a price of , while  shirts can be sold at a price of . Give a linear equation in the form  that gives the price  they can charge for  shirts.

Answer 1

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 2000 shirts can be sold at a price of $24, while 3000 shirts can be sold at a price of $17. Give a linear equation in the form p=mn+b that gives the price p they can charge for n shirts.

=>

p = price ( charge for n shirts)

n = number of shirts

m = slope of the line 

b = y intercept

 

We have 2 points here (3000, $17) and (2000, $24) which have to be on our line.

 

To find the slope m,

we use

m = (p1-p2)/(n1-n2)

m = (24-17)/(2000-3000)

                     m = 7/-1000

                     m = -0.007

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

p-p1=m(n-n1)

p-17=(-0.007)(n-3000)

p-17= -0.007n+ 21

p=-0.007n + 38

 

Tally:

we can tally our answer with other point

p=-0.007n + 38

24 =(- 0.007 x 2000) + 38

24 =-14 + 38

24 = 24 ............true