Question

Company A and Company B are combining efforts to raise money for a local family in need. Together, they hope to raise at least $800. So far, Company A has raised at least $350. The following system and graph represent this situation.

Let
represent Company A's donations and let
represent Company B's donations.



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Part I: What does the point (300,600)
represent in terms of the story situation? Is it a possible solution to the system? Why or why not?

Answer 1

To understand the point (300, 600) in the context of the situation described, we can interpret the coordinates as follows:

- The x-coordinate (300) represents the amount of money raised by Company A.
- The y-coordinate (600) represents the amount of money raised by Company B.

Thus, the point (300, 600) means that Company A has raised $300 and Company B has raised $600.

Now, to determine if (300, 600) is a possible solution to the system, we need to check two main conditions from the narrative:

1. The total amount raised by both companies (Company A and Company B combined) must be at least $800.
2. Company A's amount raised must be at least $350.

Now, let's do the calculations:

1. **Total amount raised:**
- Amount raised by Company A: $300
- Amount raised by Company B: $600
- Total: $300 + $600 = $900

The total amount raised ($900) meets the condition of being at least $800.

2. **Amount raised by Company A:**
- Amount raised by Company A: $300

However, Company A raised only $300, which does not meet the requirement of being at least $350.

Since the amount raised by Company A is less than $350, the point (300, 600) is **not a possible solution** to the system of constraints described in the story situation.