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We are given two shops, A and B, with different rental and hourly fees. We need to determine after how many hours the total rental costs at both shops will be the same.

### Shop A:
- Rental fee: \$8
- Hourly fee: \$3

### Shop B:
- Rental fee: \$4
- Hourly fee: \$4

Let $ x $ be the number of hours the kayak is rented. 

We can create equations for the total cost at each shop:

- Total cost for **Shop A**: 
  \[
  C_A = 8 + 3x
  \]
- Total cost for **Shop B**: 
  \[
  C_B = 4 + 4x
  \]

To find when the total costs are the same, we set the two equations equal:
\[
8 + 3x = 4 + 4x
\]

Now let's solve for $ x $:

\[
8 - 4 = 4x - 3x
\]
\[
4 = x
\]

So, the total costs are the same when the kayak is rented for **4 hours**.

Would you like more details or have any other questions?

### Related Questions:
1. How much will it cost to rent a kayak for 2 hours at Shop A and Shop B?
2. At what point would Shop A become cheaper than Shop B if rented for more than 4 hours?
3. How can we generalize this problem for different rental and hourly fees?
4. What is the total cost difference after renting for 5 hours at both shops?
5. If the hourly fee at Shop B increases by \$1, how does the solution change?

**Tip:** When comparing costs, setting up equations based on the given rates helps simplify the process of finding the balance point.

Two shops rent kayaks for a rental fee plus a fee per hour. How many hours must a kayak be rented for the total costs to be the same? Shop A: Rental fee: $8, Hourly fee: $3. Shop B: Rental fee: $4, Hourly fee: $4.

Learn how to solve a real-world problem comparing the rental costs of two kayak shops. The problem involves setting up and solving linear equations to find the number of hours for which the rental costs are the same. Suitable for students in Grades 6-8.

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