https://file.aiquickdraw.com/mathbot/file/17296993267549u7mdlag.jpg

Let's analyze the problem step-by-step:

1. **Constraints on Ticket Sales:**
   - We have two variables:
     - $ s $: Number of student tickets sold.
     - $ a $: Number of adult tickets sold.
   - We are given the conditions:
     - At least 500 total tickets must be sold.
     - At least \$1,750 must be raised.

2. **Expression for Total Number of Tickets Sold:**
   - The sum of student and adult tickets must be at least 500:
   \[
   s + a \geq 500
   \]

3. **Expression for Total Revenue:**
   - A student ticket costs \$2 and an adult ticket costs \$5. So, the revenue expression would be:
   \[
   2s + 5a \geq 1,750
   \]

4. **Other Basic Constraints:**
   - $ s \geq 0 $ and $ a \geq 0 $.

Now, let's fill in the blanks based on these expressions:

1. The first inequality should be $ s + a \geq 500 $.
2. The second inequality should be $ 2s + 5a \geq 1,750 $.

Thus, the correct selections should be:

- **For the first inequality:** $ s + a \geq 500 $
- **For the second inequality:** $ 2s + 5a \geq 1,750 $

Would you like any more details or have any further questions?

### Relative Questions
1. How can these inequalities be visualized on a graph?
2. What does the solution region of these inequalities represent?
3. What happens if the team sells more tickets than the minimum required?
4. How would changes in ticket prices affect the system of inequalities?
5. Can we find a specific combination of student and adult tickets that meet these requirements?

### Tip
When working with systems of inequalities, always check if both variables have realistic constraints, like non-negative values, and ensure that each condition is clearly expressed as a mathematical inequality.

Coach Van Hook’s team needs to raise at least $1,750 for new uniforms by selling student and adult tickets, where at least 500 total tickets must be sold. What system of inequalities models this situation?

Learn how to set up and solve a system of inequalities to model ticket sales for a fundraiser where a team must sell at least 500 tickets and raise at least $1,750. Explore key concepts in linear inequalities and algebraic word problems. Suitable for Grades 7-9.

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