Chapter 6.8, Problem 37PPS

(a)

To determine

To define: The variables and write a system of inequalities

Answer to Problem 37PPS

The inequalities are $x+y\le 20$ and $15x+10y\ge 90$

Explanation of Solution

Given:

Income $=\$15$ per hour as a photographer

Income $=\$10$ per hour as a coacher

Calculation:

Let $x$ represents the number of hour worked as a photographer

Let $y$ represents the number of hour worked as a coacher height and represents the weight

Now the inequalities will be $x+y\le 20$ and $15x+10y\ge 90$

Conclusion:

Hence,the inequalities are $x+y\le 20$ and $15x+10y\ge 90$

(b)

To determine

To Graph: The given system

Answer to Problem 37PPS

  

Explanation of Solution

Given:

Income $=\$15$ per hour as a photographer

Income $=\$10$ per hour as a coacher

Calculation:

The graphs will be

  

Conclusion:

Hence,the graph is drawn

(c)

To determine

To give: The two possible solutions to meet the goals

Answer to Problem 37PPS

The first possible solution to meet the goal is $6$ hours at the photographers and $10$ hours of coaching and the second possible to meet the goal is $8$ hours at the photographers and $10$ hours of coaching

Explanation of Solution

Given:

Income $=\$15$ per hour as a photographer

Income $=\$10$ per hour as a coacher

Calculation:

Here the solution is

The first possible solution to meet the goal is $6$ hours at the photographers and $10$ hours of coaching and the second possible to meet the goal is $8$ hours at the photographers and $10$ hours of coaching

Conclusion:

Hence,the sample answer is $6$ hours at the photographers and $10$ hours of coaching; $8$ hours at the photographers and $10$ hours of coaching

(d)

To determine

To find:whether the given pair is a solution or not

Answer to Problem 37PPS

The given pair $\left(2,2\right)$ is not a solution

Explanation of Solution

Given:

  $\left(2,2\right)$

Calculation:

Here the solution is

  $\left(2,2\right)$

Since the point $\left(2,2\right)$ doesn’t fall in the shaded region , she would not earn enough money

Therefore the given pair is not a solution

Conclusion:

Hence,the given pair $\left(2,2\right)$ is not a solution