A car rental shop charges a base rate plus $10 for every hour the car is being used. Rakesh rented a car for 4 hours and paid $65. What is the base rate that the car rental shop charges?

To find the base rate that the car rental shop charges, we can set up an equation based on the given information.

### Step-by-Step Solution

1. **Define Variables:**
   - Let $ B $ be the base rate (in dollars) that the car rental shop charges.
   - The shop also charges an additional $10 per hour.

2. **Formulate the Equation:**
   - Rakesh rented a car for 4 hours, so the hourly charge would be $ 10 \times 4 $.
   - The total cost Rakesh paid is $65.

   Therefore, the equation to represent this situation is:
   \[
   B + 10 \times 4 = 65
   \]

3. **Simplify the Equation:**
   \[
   B + 40 = 65
   \]

4. **Solve for $ B $:**
   \[
   B = 65 - 40
   \]
   \[
   B = 25
   \]

### Conclusion

The base rate that the car rental shop charges is **$25**.

Would you like further details or have any questions?

Here are 5 related questions to further expand your understanding:
1. What would be the total cost for renting the car for 6 hours?
2. If another customer paid $85 for renting the car, how many hours did they use it?
3. How would the equation change if the hourly rate was $15 instead of $10?
4. What is the cost function that represents the total cost as a function of hours rented?
5. If the base rate increased by $5, how would that affect the total cost for 4 hours?

**Tip:** When solving word problems, always start by defining variables and translating the given information into an equation.

Learn how to find the base rate that a car rental shop charges using a step-by-step solution. Rakesh rented a car for 4 hours and paid $65, including a base rate and an hourly charge. Suitable for Grades 6-8 students.

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