Chapter 6.6, Problem 25PPS

a.

To determine

To find: Variables and inequalities and graph of given situation.

Answer to Problem 25PPS

Variables are

‘ $x$ ’ be the square footage of the rink

‘ $y$ ’ be the price of resurfacing

Inequalities are

  $1000\le x\le 17000$ .

  $10000\le y\le 150000$ .

Explanation of Solution

Given information:

Number of Rinks used are at least 1000 square feet and upto 17,000 square feet.

Price ranges from as little as $10,000 to as much as $150,000.

Let ‘ $x$ ’ be the square footage of the rink

Let ‘ $y$ ’ be the price of resurfacing.

From given information

Number of Rinks used are at least 1000 square feet and upto 17,000 square feet.

We get

  $1000\le x\le 17000$ ---------(1)

Price ranges from as little as $10,000 to as much as $150,000

We get

  $10000\le y\le 150000$ -------(2)

Here, Black colour region represents $10000\le y\le 150000$

Blue colour region represents $1000\le x\le 17000$ -

So the solution is the common region of black colour and blue colour.

b.

To determine

To find: One possible solution.

Answer to Problem 25PPS

  $\left(10000,50000\right)$ is one possible solution.

Explanation of Solution

Given information:

Number of Rinks used are at least 1000 square feet and upto 17,000 square feet.

Price ranges from as little as $10,000 to as much as $150,000.

Inequalities are

  $\begin{array}{l}1000\le x\le 17000\\ 10000\le y\le 150000\end{array}$

Graph of given inequalities is

Here, Black colour region represents $10000\le y\le 150000$

Blue colour region represents $1000\le x\le 17000$ -

So the solution is the common region of black colour and blue colour.

As $\left(10000,50000\right)$ is present in the common region of both inequalities.

  $\left(10000,50000\right)$ is one possible solution.

c.

To determine

To find: Is $\left(15000,30000\right)$ a solution.

Answer to Problem 25PPS

Yes.

Explanation of Solution

Given information:

Number of Rinks used are at least 1000 square feet and upto 17,000 square feet.

Price ranges from as little as $10,000 to as much as $150,000.

Graph of given inequalities is

Here, Black colour region represents $10000\le y\le 150000$

Blue colour region represents $1000\le x\le 17000$ -

So the solution is the common region of black colour and blue colour.

As $\left(15000,30000\right)$ is present in the common region of both inequalities. So $\left(15000,30000\right)$ is a solution.