Chapter 6.6, Problem 37PPS

a.

To determine

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

Answer to Problem 37PPS

Variables are

‘ $x$ ’ be the number of hours worked for photographer.

‘ $y$ ’ be number of hours for coaching

Inequalities are

  $\begin{array}{l}x+y\le 20\\ 15x+10y\ge 90\end{array}$

Explanation of Solution

Given information:

Opal makes $15 per hour working for a Photographer.

Opal makes $10 per hour for coaching soccer team.

Opal needs to earn at least $90 per week

Opal does not want to work more than 20 hours per week.

Let ‘ $x$ ’ be the number of hours worked for photographer.

Let ‘ $y$ ’ be number of hours for coaching.

From given information

Opal does not want to work more than 20 hours per week.

We get

  $x+y\le 20$ -----------(1)

Opal needs to earn at least $90 per week

Money earned for working ‘ $x$ ’ hours for Photographer + Money earned for coaching ‘ $y$ ’ hours $\ge$ 90

We get

  $15x+10y\ge 90$ ----------(2)

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

b.

To determine

To find: Graph of this system.

Explanation of Solution

Given information:

Opal makes $15 per hour working for a Photographer.

Opal makes $10 per hour for coaching soccer team.

Opal needs to earn at least $90 per week

Opal does not want to work more than 20 hours per week.

Inequalities are

  $\begin{array}{l}x+y\le 20\\ 15x+10y\ge 90\end{array}$

Graph of given inequalities is

Here

Red colour represents $x+y\le 20$ .

Blue colour represents $15x+10y\ge 90$ ..

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

c.

To determine

To find: Two possible solution.

Answer to Problem 37PPS

  $\left(10,5\right)$ and $\left(7,11\right)$

Explanation of Solution

Given information:

Opal makes $15 per hour working for a Photographer.

Opal makes $10 per hour for coaching soccer team.

Opal needs to earn at least $90 per week

Opal does not want to work more than 20 hours per week.

Here

Red colour represents $x+y\le 20$ .

Blue colour represents $15x+10y\ge 90$ ..

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

As $\left(10,5\right)$ and $\left(7,11\right)$ is in the common region of Blue and Red colour.

So $\left(10,5\right)$ and $\left(7,11\right)$ are the two possible solutions.

d.

To determine

To find: Is $\left(2,2\right)$ a possible solution.

Answer to Problem 37PPS

NO

Explanation of Solution

Given information:

Opal makes $15 per hour working for a Photographer.

Opal makes $10 per hour for coaching soccer team.

Opal needs to earn at least $90 per week

Opal does not want to work more than 20 hours per week.

Here

Red colour represents $x+y\le 20$ .

Blue colour represents $15x+10y\ge 90$ ..

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

As $\left(2,2\right)$ is not present in the common region of Blue and Red colour.

So $\left(2,2\right)$ is not the solution.