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?

Question

If h represents the hourly fee, which equation models this problem?

What was the hourly fee for the rototiller?

Answer 1

To model the problem, we first need to identify the components involved in the rental cost of the rototiller. The total cost consists of an initial fixed fee plus the hourly fee multiplied by the number of hours rented.

1. Initial fee: $43
2. Hourly fee: \( h \) (this is what we want to find)
3. Number of hours rented: 7 hours
4. Total cost paid: $64

The equation that represents the total cost can be set up as follows:

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

Substituting the known values into this equation:

\[ 64 = 43 + 7h \]

Now, we can solve for \( h \):

1. Subtract 43 from both sides:

\[ 64 - 43 = 7h \]

\[ 21 = 7h \]

2. Divide both sides by 7:

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

Thus, the hourly fee is:

\[ \boxed{3} \]

In conclusion, the equation that models this problem is:

\[ 64 = 43 + 7h \]

And the hourly fee for the rototiller is \( \boxed{3} \).