https://file.aiquickdraw.com/mathbot/file/1726717191349mp4v3em9.jpg

Let's break down the problem from the image to solve it.

### Problem breakdown:
- Alex has saved **$1,500** for the picnic.
- The **park reservation fee** is **$350** (fixed cost).
- For each family invited, Alex estimates an additional **$45** for food and drinks (variable cost per family).

Let **x** represent the number of families Alex can invite.

### Linear inequality setup:
Alex's total cost must be less than or equal to his budget. The total cost includes:
- The fixed park reservation fee of **$350**.
- The variable cost of **$45** per family invited.

So, the total cost equation is:
\[
350 + 45x \leq 1500
\]
This inequality represents the situation.

### Solving the inequality:
Now, solve for $ x $ (the number of families):
\[
350 + 45x \leq 1500
\]
1. Subtract **350** from both sides:
\[
45x \leq 1150
\]
2. Divide both sides by **45**:
\[
x \leq \frac{1150}{45} \approx 25.56
\]
Since Alex can only invite a whole number of families, he can invite a maximum of **25 families**.

### Answer:
- The inequality that represents the situation is $ 350 + 45x \leq 1500 $.
- Alex can invite a maximum of **25 families** while staying within his budget.

Would you like further details or have any questions?

### Related Questions:
1. What would happen if the park fee increased to $400?
2. How many families could Alex invite if his budget increased to $1,800?
3. What if the cost per family was reduced to $40? How many families could Alex invite?
4. How would the inequality change if Alex decided to save $200 for unforeseen expenses?
5. How much additional money would Alex need to invite 30 families?

**Tip**: When solving inequalities, always check if the solution involves whole numbers, especially in practical scenarios like this one.

Alex has saved $1,500 for a community picnic he's organizing in the local park. The reservation fee for the park space is $350, and he estimates an additional $45 per family for food and drinks. How many families can Alex invite to ensure he stays within his budget? Write and solve a linear inequality to find the maximum number of families Alex can invite while staying within his budget.

Solve how many families Alex can invite to a community picnic using a $1,500 budget with a fixed park fee of $350 and $45 per family for food. Learn how to set up and solve the inequality 350 + 45x ≤ 1500. Suitable for students in Grades 7-9.

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