Question

A clothing business finds there is a linear relationship between the number of shirts, n (in thousands) it can sell and the price, P, it can charge per shirt. In particular, historical data shows that 3 thousand shirts can be sold at a price of $69 each, and that 7 thousand shirts can be sold at a price of $61 each Find the equation of the form P(n)=mn+b that gives the price P they can charge for n thousand shirts.

Answer 1

Answer:

$P(n)=-2n+75$

Step-by-step explanation:

Let n represent the number of shirts in thousands and P represent the charge per shirt. n is the independent variable and P is the dependent variable.

Since 3000 shirts sell for $69 each, this can be represented as (3, 69). Also 7000 shirts sell for $61 each, this can be represented as (7, 61).

The equation showing the relationship is gotten using:

$P-P_1=\frac{P_2-P_1}{n_2-n_1}(n-n_1) \\\\P-69=\frac{61-69}{7-3} (n-3)\\\\P=-2(n-3)+69\\\\P=-2n+75\\\\P(n)=-2n+75$