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 x
represent Company A's donations and let y
represent Company B's donations.

image.png
x+y≥800
x≥350

Part II: What does the point 500,400
represent in terms of the story situation? Is it a possible solution to the system? Why or why not?

Answer 1

The point (500, 400) represents a specific donation scenario where Company A raises $500 and Company B raises $400.

To determine if this point is a possible solution to the system, we need to check if it satisfies both inequalities in the system:

1. Check the first inequality \( x + y \geq 800 \):
- Substitute \( x = 500 \) and \( y = 400 \):
\[
500 + 400 = 900
\]
- Since \( 900 \geq 800 \), this condition is satisfied.

2. Check the second inequality \( x \geq 350 \):
- Substitute \( x = 500 \):
\[
500 \geq 350
\]
- This condition is also satisfied.

Since both inequalities are satisfied by the point (500, 400), it is indeed a possible solution to the system.