Question

PLEASE HELP ASAP!!!!Mark is trying to earn at least $160 per week between his two part-time jobs. He earns $10 per hour cleaning houses and $8 per hour filing papers at his mom's business. He can work a maximum of 25 hours per week.

Answer 1

Explanation:

Then he should work for 10 hours for house cleaning = 100$

And he should work to fill papers for 8 hours = 64$

Total 18 hours a week and 164$ made.

I hope it helps

Answer 2

We know that

• Mark earns $10 per hour of cleaning houses.

,

• He earns $8 per hour filing papers.

,

• He can work a maximum of 25 hours per week.

,

• He wants to earn at least $160 per week.

Let's call x the hour of cleaning houses, and y the hour filing papers.

Using the given information, we can express the following.

`\begin{gathered} 10x+8y\ge160 \\ x+y\leq25 \end{gathered}`

The first inequality is about the earnings, and the second inequality is about the hours per week.

Then, to find the solution, we have to graph each inequality. To graph them, we have to find the axis interceptions of each of them.

For the first expression, we have.

x = 0.

`\begin{gathered} 10\cdot0+8y=160 \\ 8y=160 \\ y=(160)/(8)=20 \end{gathered}`

The y-intercept is (0, 20).

y = 0.

`\begin{gathered} 10x+8\cdot0=160 \\ 10x=160 \\ x=(160)/(10) \\ x=16 \end{gathered}`

The x-interception is (16, 0).

Then, we graph both points and draw a straight line through them. Notice that the first expression has the relation "greater than or equal to" which means the solution area would be above the line. The following image shows the graph.

Similarly, we repeat the process for the second inequality. We have to graph on top of the first graph.

x = 0.

`\begin{gathered} 0+y=25 \\ y=25 \end{gathered}`

The y-intercept is (0, 25).

y = 0.

`\begin{gathered} x+0=25 \\ x=25 \end{gathered}`

The x-intercept is (25, 0).

The image below shows both inequalities.