
Stefan’s family rented a rototiller to prepare an area in their backyard for spring planting. The rental company charged an initial fee of $43 with an additional fee per hour. If they paid $64 after renting the rototiller for 7 hours, what was the hourly fee?
If h represents the hourly fee, which equation models this problem?

What was the hourly fee for the rototiller?


Let's break down the problem step by step.

### Given:
- Initial fee (fixed cost): $43
- Total amount paid: $64
- Number of hours rented: 7 hours
- Hourly fee: $ h $ (this is what we need to find)

### Step 1: Set up the equation
The total cost is the sum of the initial fee and the cost for the number of hours rented. This can be modeled by the following equation:

\[
\text{Total cost} = \text{Initial fee} + (\text{Hourly fee} \times \text{Number of hours})
\]

Substituting the given values:

\[
64 = 43 + 7h
\]

### Step 2: Solve for $ h $
To find the hourly fee $ h $, subtract 43 from both sides of the equation:

\[
64 - 43 = 7h
\]

\[
21 = 7h
\]

Now, divide both sides by 7:

\[
h = \frac{21}{7} = 3
\]

### Answer:
The hourly fee for the rototiller is **$3**.

### Equation that models the problem:
\[
64 = 43 + 7h
\]

Do you want more details or have any questions?

### Related Questions:
1. What would be the total cost if they rented the rototiller for 10 hours?
2. If the hourly fee increased by $1, what would be the new total cost for 7 hours?
3. How many hours could they rent the rototiller if their budget was $100?
4. What would be the initial fee if the total cost for 7 hours was $80?
5. If the total amount paid was $50 after renting for 5 hours, what would the hourly fee be?

### Tip:
Always verify your final answer by substituting it back into the original equation to ensure it satisfies the problem conditions.

Stefan’s family rented a rototiller to prepare an area in their backyard for spring planting. The rental company charged an initial fee of $43 with an additional fee per hour. If they paid $64 after renting the rototiller for 7 hours, what was the hourly fee? If h represents the hourly fee, which equation models this problem? What was the hourly fee for the rototiller?

Learn how to solve a linear equation to find the hourly fee of a rototiller. In this example, Stefan’s family rented a rototiller with an initial fee of $43 and paid $64 after 7 hours. Follow a step-by-step guide to set up the equation and calculate the hourly rate. Suitable for Grades 6-8.

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