1. Estimate the Ordered Pair Where the Lines Intersect and Its Meaning

By examining the graph, the estimated point of intersection appears to be approximately (100, 75).

Interpretation:

• The x-coordinate (100) represents the number of hours worked at the $8.25/hour job.
• The y-coordinate (75) represents the number of hours worked at the $9.00/hour job.

This intersection point represents a combination of hours worked at both jobs that allows you to meet the income requirement of $1,475 per month while staying within the monthly work limit of 172 hours.

2. Possible Solution for the System of Inequalities and Its Meaning

The system of inequalities given is:

1. $x + y \leq 172$ (Total hours limit)
2. $8.25x + 9.00y \geq 1475$ (Income requirement)

A possible solution is the ordered pair (100, 75).

Interpretation:

• Working 100 hours at the $8.25/hour job and 75 hours at the $9.00/hour job will allow you to meet or exceed the income requirement of $1,475 without exceeding the maximum allowed working hours.

3. How Many Hours Would You Work at Each Job Per Week?

There are 4.3 weeks in a month.

• Hours at the $8.25/hour job:
  $\frac{100}{4.3} \approx 23.26 \, \text{hours/week}$

• Hours at the $9.00/hour job:
  $\frac{75}{4.3} \approx 17.44 \, \text{hours/week}$

Justification:
Working approximately 23 hours/week at the $8.25/hour job and 17 hours/week at the $9.00/hour job keeps you under the 40-hour weekly limit and ensures you earn at least $1,475/month.

Would you like a more detailed breakdown or further clarification?

Related Questions:

1. What is the total income generated by working 100 hours at $8.25/hour and 75 hours at $9.00/hour?
2. How would your work schedule change if the pay rate for the second job increased to $10/hour?
3. If you could work an extra 10 hours per month, how would that impact your income?
4. What would happen if your total allowed work hours per month decreased to 160 hours?
5. How can you adjust your work hours to save for unexpected expenses?

Tip:
Balancing work and study is essential. Consider allocating more hours to the higher-paying job if possible to reduce total working hours while meeting financial goals.