Chapter 6.6, Problem 9CYU

a.

To determine

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

Answer to Problem 9CYU

Variables are

‘ $w$ ’ be the weight.

‘ $h$ ’ be the height

Inequalities are

  $\begin{array}{l}h<79\\ w<295\end{array}$

Explanation of Solution

Given information:

Height must be under = 6 ft 7 inches.

Weight must be under =295 lb.

We know

1feet =12 inches

Therefore

6 feet 7 inches = 6 feet + 7 inches

  = $6\left(12\right)+7$

  = $72+7$

  =79 inches

Let ‘ $w$ ’ be the weight.

Let ‘ $h$ ’ be the height.

From the given information

Height must be less than 79 inches

Therefore

  $h<79$ -----------(1)

Weight must be less than 295 lb.

Therefore

  $w<295$ ----------(2)

Equations-(1) and (2) represents the inequalities of above situation.

  

Here

Blue colour represents the region of $w<295$

Red colour represents the region of $h<79$ .

Common region of Red colour and Blue colour represent the solution of above inequalities.

b.

To determine

To find: One possible solution.

Answer to Problem 9CYU

  $\left(65,200\right)$

Height = 65 inches.

Weight = 200 lb.

Explanation of Solution

Given information:

Height must be under = 6 ft 7 inches.

Weight must be under =295 lb.

Inequalities are

  $\begin{array}{l}h<79\\ w<295\end{array}$

Graph of given inequalities is

  

Blue colour represents the region of $w<295$

Red colour represents the region of $h<79$ .

Common region of Red colour and Blue colour represent the solution of above inequalities.

As $\left(65,200\right)$ is present in the common region of both inequalities.

  $\left(65,200\right)$ is one possible solution.

c.

To determine

To find:Is $\left(50,180\right)$ a solution.

Answer to Problem 9CYU

Yes.

Explanation of Solution

Given information:

Height must be under = 6 ft 7 inches.

Weight must be under =295 lb.

Graph of given inequalities is

  

Blue colour represents the region of $w<295$

Red colour represents the region of $h<79$ .

Common region of Red colour and Blue colour represent the solution of above inequalities.

As $\left(50,180\right)$ is present in the common region of both inequalities. So $\left(50,180\right)$ is a solution.