https://file.aiquickdraw.com/mathbot/file/1726575758175vi8kp2ic.jpg

Let's analyze the problem in the image and work through the inequality.

### Problem Breakdown:
- **Annual Pass**: Costs $385 plus $10 per day for parking.
- **Regular Visit Cost**: $26 per day for tickets and an extra $15 for parking.

Miguel wants to know how many days ($d$) he would need to visit for the annual pass to be cheaper than paying daily for each visit.

### Equation Setup:
- **Cost for the Annual Pass** (with $d$ days of parking): $385 + 10d$
- **Cost for Regular Daily Visits** (with $d$ days): $26d + 15d = 41d$

We want to find when the cost of the annual pass is less than the daily visit cost:
\[
385 + 10d < 41d
\]

Now, let's solve this inequality:
\[
385 + 10d < 41d
\]
Subtract $10d$ from both sides:
\[
385 < 31d
\]
Divide both sides by 31:
\[
d > \frac{385}{31} \approx 12.42
\]
So, Miguel would need to visit the park at least **13 days** for the annual pass to be cheaper.

### Correct Answer:
The inequality that models this situation is:
\[
385 + 10d < 41d
\]
which corresponds to **Option A**.

Would you like a detailed explanation of any part of the process?

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Here are 5 related questions to expand your understanding:
1. What happens if parking costs are higher on some days?
2. How would the inequality change if the daily ticket prices increase by 10%?
3. What if the annual pass had a discounted price?
4. How can you solve this inequality using graphing methods?
5. How would a fixed parking cost (no daily charge) affect the problem?

**Tip**: When solving inequalities, always double-check the direction of the inequality after dividing or subtracting terms!

Miguel loves to visit a local amusement park and is considering purchasing an annual pass, which costs $385, plus an extra $10 per day for parking. Tickets regularly cost $26 per day plus an extra $15 for parking. Miguel wants to know how many days he would have to visit the amusement park for the annual pass to cost less than paying per daily visit. Identify the inequality Miguel can use to model this problem.

Learn how to set up and solve an inequality comparing the cost of an annual pass versus daily visits to an amusement park. This problem includes concepts of inequalities, linear equations, and cost analysis, suitable for students in Grades 6-8.

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