https://file.aiquickdraw.com/mathbot/file/1725581591158ygbcb72b.jpg

The problem presented in the image can be summarized as follows:

A car rental company offers two plans for renting a car:
- **Plan A**: $30 per day plus 10 cents per mile.
- **Plan B**: $60 per day with unlimited mileage.

The question asks how many miles you would need to drive in one day for Plan B to save you money compared to Plan A. The inequality should be set up using the variable $ x $ to represent the number of miles.

### Solution:

Let $ x $ represent the number of miles driven.

**Cost of Plan A**: 
The total cost of Plan A would be:
\[
\text{Cost of Plan A} = 30 + 0.10x
\]

**Cost of Plan B**: 
The total cost of Plan B is fixed at $60.

We want to find when Plan B saves money, meaning:
\[
\text{Cost of Plan B} < \text{Cost of Plan A}
\]
\[
60 < 30 + 0.10x
\]

### Solving the inequality:
\[
60 - 30 < 0.10x
\]
\[
30 < 0.10x
\]
\[
x > \frac{30}{0.10}
\]
\[
x > 300
\]

Thus, you would need to drive **more than 300 miles** for Plan B to save you money compared to Plan A.

### Final Answer:
You need to drive more than **300 miles** in a day for Plan B to be the cheaper option.

---

Do you want more details or have any questions about this? 

Here are 5 related questions:
1. How would the inequality change if Plan A’s cost per mile increased to 15 cents per mile?
2. What if Plan B's daily rate was reduced to $50? How would that affect the break-even point?
3. Can you set up the equation to find when Plan A and Plan B cost the same?
4. How would the result change if you rented the car for multiple days instead of just one?
5. What happens if you drive fewer than 300 miles in a day? Which plan would be cheaper?

**Tip**: When comparing two pricing plans, always set up an inequality or equation to help determine the break-even point or best option based on different variables like miles driven or days rented.

A car rental company offers two plans for renting a car. Plan A: $30 per day and 10 cents per mile. Plan B: $60 per day with unlimited mileage. How many miles would you need to drive in one day for Plan B to save you money? Set up the inequality using x to represent the number of miles.

Learn how to compare car rental plans with a simple inequality. This problem explains how to determine the number of miles at which an unlimited mileage plan becomes the cheaper option. Great for students in Grades 6-8 who are learning algebra and inequality solving techniques.

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