Chapter 8.8, Problem 25E

a.

To determine

To write:

A system of equations describing the total cost of buying and operating each printer.

Answer to Problem 25E

Our required system of equations would be:

  $\begin{array}{l}y=0.15x+100\\ y=0.03x+400\end{array}$

Explanation of Solution

Given:

You are trying to decide whether to buy an inkjet printer for $100 or a laser printer for $400. The operating costs are estimated to be $0.15 per page for the inkjet printer and $0.03 per page for the laser printer.

Calculation:

Letxrepresent number of pages and y represent total cost.

The cost of printing x pages by inkjet printer would be $0.15x$ . The total cost of printing x pages by inkjet printer would be $0.15x$ plus inkjet printer’s cost. We can represent this information in an equation as:

  $y=0.15x+100$

The cost of printing x pages by laser printer would be $0.03x$ . The total cost of printing x pages by laser printer would be $0.03x$ plus laser printer’s cost. We can represent this information in an equation as:

  $y=0.03x+400$

Therefore, our required system of equations would be:

  $\begin{array}{l}y=0.15x+100\\ y=0.03x+400\end{array}$

b.

To determine

To solve:

The system of equations using a graphing calculator. After how many pages are the total costs of the printers equal.

Answer to Problem 25E

The total costs of both printers will be equal after 2500 pages.

Explanation of Solution

Given:

You are trying to decide whether to buy an inkjet printer for $100 or a laser printer for $400. The operating costs are estimated to be $0.15 per page for the inkjet printer and $0.03 per page for the laser printer.

Calculation:

Using an online graphing tool, we will get:

  

We can see that both lines intersect at $(2500,475)$ . Therefore, the total costs of both printers will be equal after 2500 pages.

c.

To determine

To solve:

The system of equations using the given verbal model.

Answer to Problem 25E

The total costs of both printers will be equal after 2500 pages.

Explanation of Solution

Given:

You are trying to decide whether to buy an inkjet printer for $100 or a laser printer for $400. The operating costs are estimated to be $0.15 per page for the inkjet printer and $0.03 per page for the laser printer.

  

Calculation:

To solve the given system of equations, we will equate both equations as:

  $0.15x+100=0.03x+400$

Let us solve for x .

  $\begin{array}{l}0.15x-0.03x+100=0.03x-0.03x+400\\ 0.12x+100=400\\ 0.12x+100-100=400-100\\ 0.12x=300\\ \frac{0.12x}{0.12}=\frac{300}{0.12}\\ x=2500\end{array}$

Therefore, the total costs of both printers will be equal after 2500 pages.

d.

To determine

To compare and contrast:

The methods used in part (b) and part (c). When would you use each method?

Explanation of Solution

Given:

You are trying to decide whether to buy an inkjet printer for $100 or a laser printer for $400. The operating costs are estimated to be $0.15 per page for the inkjet printer and $0.03 per page for the laser printer.

  

Calculation:

We can see that we got same answer using graphing method and solving the system algebraically.

We will use graphing method when the equations contain complicated expressions.

We will solve system of equations manually, when the equations contain easy numbers and are easily computable.