Chapter 6.6, Problem 48PFA

a.

To determine

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

Answer to Problem 48PFA

Variables are

‘ $w$ ’ be the width of the playground.

‘ $l$ ’ be the length of the playground.

Inequalities are

  $\begin{array}{l}w\ge 100\\ l+w\le 175\end{array}$

Explanation of Solution

Given information:

Width of one side of fencing had to be at least 100 yards.

Total fencing around the play ground had to be no more than 350 yards.

Let

‘ $w$ ’ be the width of the playground.

‘ $l$ ’ be the length of the playground.

From given information

Width of one side of fencing had to be at least 100 yards.

We get

  $w\ge 100$ ---------(1)

Total fencing around the playground had to be no more than 350 yards.

We get

  $2\left(l+w\right)\le 350$

  $\Rightarrow l+w\le 175$ -------------(2)

Equation-(1) and Equation-(2) represents system of inequalities of given situation.

b.

To determine

To find: Select all possible solutions.

Answer to Problem 48PFA

  $\left(25,150\right)$ , $\left(50,125\right)$ , $\left(70,100\right)$ , $\left(75,100\right)$ .

Are the possible solutions.

Explanation of Solution

Given information:

Width of one side of fencing had to be at least 100 yards.

Total fencing around the playground had to be no more than 350 yards.

Inequalities are

  $\begin{array}{l}w\ge 100\\ l+w\le 175\end{array}$

Given points $\left(l,w\right)$ are

  $\left(70,100\right)$ , $\left(75,105\right)$ , $\left(80,100\right)$ , $\left(85,85\right)$ , $\left(25,150\right)$ , $\left(50,125\right)$ , $\left(75,100\right)$

Graph of given inequalities is

  

Here

Red colour represents region of inequality $w\ge 100$ .

Blue colour represents $l+w\le 175$ .

Common region of Red colour, Blue colour is the solution of above inequalities.

So only points $\left(25,150\right)$ , $\left(50,125\right)$ , $\left(70,100\right)$ , $\left(75,100\right)$ .

c.

To determine

To find: Is $\left(-50,225\right)$ solution or not.

Answer to Problem 48PFA

No

Explanation of Solution

Given information:

Width of one side of fencing had to be at least 100 yards.

Total fencing around the playground had to be no more than 350 yards.

Given point is $\left(l,w\right)=\left(-50,225\right)$ .

Here length = -50

As length cannot be negative.

So $\left(-50,225\right)$ is not a possible solution