A clothing business finds there is a linear relationship bet

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 3000 shirts can be sold at a price of $59, while 5000 shirts can be sold at a price of S43. Give a linear equation in the form p - mn b that gives the price p they can charge for n shirts

Solution

n = number of shirts
p = price of a shirt

Since the relationship is linear and the equation is of the form:
p=mn+b we will find m first. We have two values of p and two of m.
They can be expressed as cartesian coordinates:

(3000, 59) and (5000, 43)
For our equation:
(p2 - p1) = m(n2 - n1)
(59 - 43) = m(3000 - 5000)
m = (59 - 43)/(3000 - 5000)
m = -16/2000
m = -1/125

So the equation becomes:
p = (-1n/125) + b

Now to find b. Use either point:
59 = [-1*(3000)/125] + b
b - 24 = 59
b = 83 So the equation becomes:
p = (-n/125) + 83