Chapter 6.6, Problem 26PPS

a.

To determine

To find: System of inequalities of given situation.

Answer to Problem 26PPS

Inequalities are

  $10\le h\le 30$

  $d\ge 6.50h$

Explanation of Solution

Given information:

Amount of time Josefina works = 10 to 30 hours.

She earns $6.50 per hour and tips.

‘ $d$ ’ be number of dollars she earns for working ‘ $h$ ’ hours.

From given information

Amount of time Josefina works = 10 to 30 hours.

We get

  $10\le h\le 30$ -------------(1)

She earns $6.50 per hour and tips

It means

  $d\ge 6.50h$ -----------(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:

Amount of time Josefina works = 10 to 30 hours.

She earns $6.50 per hour and tips.

‘ $d$ ’ be number of dollars she earns for working ‘ $h$ ’ hours.

Inequalities are

  $\begin{array}{l}d\ge 6.50h\\ 10\le h\le 30\end{array}$

Graph of given inequalities is

  

Here

Red colour represents $10\le h\le 30$ .

Blue colour represents $d\ge 6.50h$ .

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

c.

To determine

To find:How many hours did Josefina work.

Answer to Problem 26PPS

25 hours.

Explanation of Solution

Given information:

Amount of time Josefina works = 10 to 30 hours.

She earns $6.50 per hour and tips.

Tips received by Josefina = $17.50

Total amount received by Josefina for the week = $180

We know

Total amount = Amount for hourly wages + Amount of tips

Form given information

Tips received by Josefina = $17.50

Total amount received by Josefina for the week = $180

We know hourly wages = 6.50h

On substituting

We get

  $\begin{array}{l}\Rightarrow 180=6.50h+17.50\\ \Rightarrow 6.50h=180-17.50\\ \Rightarrow 6.50h=162.5\\ \Rightarrow h=\frac{162.5}{6.50}\\ \Rightarrow h=25\end{array}$

Therefore

Number of hours Josefina works = 25