Chapter 5.7, Problem 30E

To determine

To write and graph the inequality that represents the situation.

Explanation of Solution

Given:

The working time is no more than $20$ hours and earnings of at least $\$120$ and required to work at least $8$ hours in grocery store.

Calculation:

Let the number of hours worked in grocery store be $x$

And the number of hours teaching music lessons be $y$

Therefore, as per the question, the following inequality can be formed-

  $\begin{array}{l}x+y\le 20\\ 10x+15y\ge 120\\ x\ge 8\end{array}$

The following is the graph-

To determine

To identify and interpret the solution of the system.

Answer to Problem 30E

  $(14,4)$

Explanation of Solution

Given:

The large box weigh $75$ pounds and small box weigh $40$ pounds and weight limit is $2000$ lb.

Calculation:

The following is the system of inequalities-

  $\begin{array}{l}x+y\le 20\\ 10x+15y\ge 120\\ x\ge 8\end{array}$

On solving them the solution is $(14,4)$ that is $14$ hours working at the grocery store and $4$ hours teaching music lessons.

To determine

To use the graph to tell whether you can work for $8$ hours at the grocery store and teach $1$ hour of music lessons.

Answer to Problem 30E

No.

Explanation of Solution

Given:

The large box weigh $75$ pounds and small box weigh $40$ pounds and weight limit is $2000$ lb.

Calculation:

No, because point $(8,1)$ is not on the shaded region.