Chapter 1.3, Problem 9E

To determine

The newspaper that charges less per line, then to find the number of lines for which the total costs would be same for both newspapers.

Answer to Problem 9E

Greenville Journal charges less per line.

When lines will be $5$ , total cost would be same.

Explanation of Solution

Given information: Table for Daily Times and equation $y=2x+20$ for Greenville Journal.

Calculation:

Point slope form: $y-y_1=m(x-x_1)$

Calculating slope for Daily Times,

  $m=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}m=\frac{39-27}{8-4}\\ \\ m=\frac{12}{4}\\ \\ m=3\end{array}$

Considering the point $(4,27)$ and substituting the values to derive point-slope form,

  $\begin{array}{l}y-y_1=m(x-x_1)\\ \\ y-27=3(x-4)\\ \\ y=3x-12+27\\ \\ y=3x+15\end{array}$

As the slope of Greenville Journal is less than Daily Times $(2<3)$ , it charges less per line.

For total costs to be same,

  $\begin{array}{l}2x+20=3x+15\\ \\ x=5\end{array}$

Thus, when lines will be $5$ , total cost would be same.