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Let's solve the given problem step-by-step.

### Problem:
- **40% of a number** is subtracted from **120**.
- The result is **26.66% of the same number**.
- We need to **find the original number**.

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### Solution:

Let the unknown number be \( x \).

1. **40% of the number:**  
   \( 40\% \, \text{of} \, x = 0.4x \)

2. **Equation setup:**  
   Subtracting \( 0.4x \) from 120 gives \( 26.66\% \) of the same number:
   \[
   120 - 0.4x = 0.2666x
   \]
   (Note: \( 26.66\% \) as a decimal is \( 0.2666 \)).

3. **Rearrange the equation:**
   \[
   120 = 0.4x + 0.2666x
   \]
   Combine like terms:
   \[
   120 = 0.6666x
   \]

4. **Solve for \( x \):**
   \[
   x = \frac{120}{0.6666} \approx 180
   \]

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### Final Answer:
The original number is approximately **180**.

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Do you need further details or have any questions?

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Here are 5 related questions to deepen your understanding:
1. What happens if the percentage values are changed? Can the same method be used?
2. How do we handle cases where the result is a fraction of a different number?
3. What is the impact of rounding decimals like \( 26.66\% \) on calculations?
4. How would you write this equation if the unknown value were in a different position?
5. Can you express the problem in terms of ratios instead of percentages?

**Tip:** When dealing with percentages in equations, always convert them to decimals to simplify calculations.

When 40% of a number is subtracted from 120, the answer is 26.66% of the number. Find the number.

Learn how to solve a math problem involving percentages and equations. The problem asks to find a number where 40% of it subtracted from 120 equals 26.66% of the same number. Ideal for students in Grades 8-10, the solution explores algebra and percentage applications.

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