Question

Nancy needs to earn at least $60 per day. She gets $10 per hour as a babysitter and $20per hour as a sales person. If she can work at most 5 hours per day, identify the system ofinequalities and the corresponding graph that determine when Nancy will be able to meether goal.

Answer 1

`\begin{gathered} b+s\le5 \\ 10b+20s\ge60 \end{gathered}`

Check the graph below, please.

1) From the data we can write out the following system of linear inequalities, say b for babysitting and "s" as a saleswoman:

`\begin{gathered} b+s\le5 \\ 10b+20s\ge60 \end{gathered}`

Note that the first inequality refers to the number of hours per day she can work, and the second inequality refers to her need of making money per day as well.

2) We can graph this system, as below:

Since the common region is the solution is the darker one, we can locate the following point as a possible solution below:

So as we can see the point (1, 3) is a possible solution for Nancy working 1 hour as a babysitter and three hours as a saleswoman:

`\begin{gathered} b+s\le5 \\ 1+3\le5 \\ \\ 10b+20s\ge60 \\ 10(1)+20(3)\ge60 \\ 70\ge60 \end{gathered}`

3) Hence, the Linear System of inequalities is:

`\begin{gathered} b+s\le5 \\ 10b+20s\ge60 \end{gathered}`