Chapter 8.8, Problem 27E

a.

To determine

To write:

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

Answer to Problem 27E

Our required system of equations would be:

  $\begin{array}{l}l=2w\mathrm{...}(1)\\ l=\frac{450}{w}\mathrm{...}(2)\end{array}$

Explanation of Solution

Given:

You are designing a reflecting pool for a park. The design specifications say that the area of the pool should be 450 square feet. You want the pool to be rectangular and have a length that is twice the width.

Calculation:

Letlbe pool’s length and w be pool’s width.

We have been given that the length of pool is twice the width. We can represent this information in an equation as:

  $l=2w$

We are also told that area of the pool should be 450 square feet. We know that are of rectangle is length times width. We can represent this information in an equation as:

  $l\cdot w=450$

Let us solve for l .

  $\begin{array}{l}\frac{l\cdot w}{w}=\frac{450}{w}\\ l=\frac{450}{w}\end{array}$

Therefore, our required system of equations would be:

  $\begin{array}{l}l=2w\mathrm{...}(1)\\ l=\frac{450}{w}\mathrm{...}(2)\end{array}$

b.

To determine

To use:

The table feature to make a table of solutions for each equation. What ordered pair $(w,l)$ has positive coordinates and satisfies both equations. What should the dimensions of the reflecting pool be?

Answer to Problem 27E

The length of the pool would be 30 feet and width of the pool would be 15 feet.

Explanation of Solution

Given:

You are designing a reflecting pool for a park. The design specifications say that the area of the pool should be 450 square feet. You want the pool to be rectangular and have a length that is twice the width.

Calculation:

Using TI 84, we will get our required table as:

  

Upon looking at our table, we can see that the value of equations is same, when the value of independent variable is 15.

The ordered pair $(15,30)$ satisfies both equations.

Therefore, the length of the pool would be 30 feet and width of the pool would be 15 feet.