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.

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 $x$: $x = \frac{120}{0.6666} \approx 180$

Final Answer:

The original number is approximately 180.

Do you need further details or have any questions?

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.