Chapter ISG, Problem 6.8STP

To determine

To write the system of inequalities

Answer to Problem 6.8STP

  $x+y\le 20$

  $12x+18y\ge 280$

Explanation of Solution

Given:

Money earned by hardware store=$12

Money earned as lifeguard=$18

Maximum number of working hours=20

Calculation:

Let the number of hours worked at hardware store be $x$ and number of hours worked as lifeguard be $y$ .

According to question,

  $x+y\le 20$   (1)

And

  $12x+18y\ge 280$   (2)

Hence, these are the system of inequalities.

To determine

To graph the system

Explanation of Solution

Given:

Equations of system

Graph:

  

Interpretation:

The green line represents $x+y\le 20$

The blue line represents $12x+18y\ge 280$

To determine

To find if working at store is enough

Answer to Problem 6.8STP

Explanation of Solution

Given:

Money earned by hardware store=$12

Money earned as lifeguard=$18

Maximum number of working hours=20

Calculation:

We know that,

  $x+y\le 20$

And

  $12x+18y\ge 280$

To find the desired situation, put y =0 and x =20

So, $12x+18y$ is the left hand side,

Solving after putting the values,

  $12(20)+18(0)$

Hence,

  $240$ which is less than right hand side,

So, the least amount cannot be earned by working at hardware store only.

Graph:

  

Interpretation:

As you can see, the point of intersection is at 4^th quadrant, meaning both values are negative, hence, solution of this isn’t real.