https://file.aiquickdraw.com/mathbot/file/17302464342918syt7gkt.jpg

Let's go through the problem step by step.

### Part (a)
We are given:
- The initial length of the rope is represented by \( L \) (in meters).
- The magician makes the rope 3.6 meters longer.
- The final length of the rope becomes 8.49 meters.

To set up an equation:
1. Since the rope length increases by 3.6 meters, we add 3.6 to \( L \).
2. This sum equals the final length of 8.49 meters.

Thus, the correct equation is:
\[
L + 3.6 = 8.49
\]

### Part (b)
To solve for \( L \), we need to isolate \( L \) in the equation \( L + 3.6 = 8.49 \).

1. Subtract 3.6 from both sides:
   \[
   L = 8.49 - 3.6
   \]
2. Calculate the result:
   \[
   L = 4.89
   \]

So, the length of the rope at the beginning of the trick is **4.89 meters**.

Would you like further details on the solution process, or do you have any questions?

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### Related Questions:
1. How would the equation change if the rope length decreased by 3.6 meters instead?
2. What if the final length of the rope were doubled after the addition?
3. How would you verify the solution by substituting \( L \) back into the equation?
4. What happens if an additional length of rope (e.g., 1 meter) is added after the final 8.49 meters?
5. How can you set up similar equations for other real-world scenarios with different units?

### Tip:
When setting up equations, clearly define your variable and carefully determine if you’re adding or subtracting values based on the context.

At the beginning of a trick, a magician holds up a piece of rope. Then she magically makes the rope 3.6 meters longer. The final length of the rope is 8.49 meters. Write an equation to find the initial length of the rope.

Learn how to solve a real-world problem involving linear equations, where the initial length of a rope is found after it increases by 3.6 meters to reach a final length of 8.49 meters. Ideal for Grade 7-8 students.

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