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Let's break down the problem to find how many people Steve and Michelle can invite while staying within their budget.

### Problem Details:
- Total budget: $2000
- Reception hall charges:
  - Cleanup fee: $90
  - Cost per person: $33

We need to calculate the greatest number of people they can invite, denoted as $ x $.

### Step-by-Step Approach:
1. **Total Cost Formula**:  
   The total cost is given by the cleanup fee plus the cost per person multiplied by the number of people:  
   \[
   \text{Total Cost} = 90 + 33x
   \]
2. **Set up the inequality**:  
   The total cost must be less than or equal to the budget ($2000):  
   \[
   90 + 33x \leq 2000
   \]
3. **Solve for $ x $**:  
   Subtract 90 from both sides:  
   \[
   33x \leq 2000 - 90
   \]
   \[
   33x \leq 1910
   \]
   Now, divide by 33:  
   \[
   x \leq \frac{1910}{33} \approx 57.88
   \]
4. **Conclusion**:  
   Since we need to round down to the nearest whole person, $ x = 57 $.

Thus, Steve and Michelle can invite **57 people** to the reception.

Would you like more details on any step? Here are some related questions:

1. How would the solution change if the cleanup fee were higher?
2. What if they had a different budget, say $2500?
3. How many people could they invite if the cost per person increased to $40?
4. What if they didn't have a cleanup fee, how many people could they invite?
5. How would the number of people change if the budget was set in euros instead of dollars?

**Tip**: When solving inequalities, always check if rounding is necessary, especially when dealing with real-life situations where partial answers don't make sense.

Steve and Michelle Neely are celebrating their 30th anniversary by having a reception at a local reception hall. They have budgeted $2000 for their reception. If the reception hall charges a $90 cleanup fee plus $33 per person, find the greatest number of people that they may invite and still stay within their budget.

Find out how many guests Steve and Michelle can invite to their 30th anniversary reception while staying within their $2000 budget. Learn how to set up and solve linear inequalities, accounting for a $90 cleanup fee and a $33 per person cost. This is a practical application of algebra for students in Grades 7-9.

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