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We are comparing two car rental plans to determine for what mileage Plan B saves money over Plan A. Let's break down the problem:

- **Plan A:** Costs \$30 per day + 14 cents (or \$0.14) per mile.
- **Plan B:** Costs \$50 per day with free unlimited mileage.

We need to find the number of miles, $ x $, at which Plan B becomes cheaper than Plan A.

### Step-by-step approach:
1. **Cost of Plan A:**  
   The cost depends on the number of miles driven.  
   \[
   \text{Cost of Plan A} = 30 + 0.14x
   \]
   where $ x $ is the number of miles driven.

2. **Cost of Plan B:**  
   The cost is fixed at \$50, regardless of mileage.  
   \[
   \text{Cost of Plan B} = 50
   \]

3. **Set up inequality:**  
   We need to find when Plan B is cheaper than Plan A:
   \[
   50 < 30 + 0.14x
   \]

4. **Solve for $ x $:**
   \[
   50 - 30 < 0.14x
   \]
   \[
   20 < 0.14x
   \]
   \[
   x > \frac{20}{0.14} = 142.86
   \]

### Conclusion:
To save money with Plan B, you must drive more than **142.9 miles**.

Do you need further details or clarifications? Here are five related questions you might find useful:
1. How would the solution change if Plan A charged 10 cents per mile instead of 14 cents?
2. What is the cost of each plan if you drive exactly 142.9 miles?
3. How does the cost difference between the plans change for every additional 10 miles?
4. What if Plan B reduced its daily cost to \$45? How would that impact the mileage comparison?
5. How can you model this situation using a graph to visualize the break-even point?

**Tip:** Always check the mileage when selecting car rental plans to see if you're getting the best deal, especially for long-distance trips!

A car rental company offers two plans for renting a car. Plan A: 30 dollars per day and 14 cents per mile. Plan B: 50 dollars per day with free unlimited mileage. For what range of miles will plan B save you money? To save money the mileage must be greater than _____.

Discover how to compare two car rental plans using algebraic inequalities. Learn when Plan B, with a fixed cost of 50 dollars, becomes cheaper than Plan A, which charges 30 dollars per day plus 14 cents per mile. Suitable for Grades 7-10.

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