What is the percentage change in the result when we add 50 to a certain number x, instead of subtracting 50 from the same number x?

Options

A. `50%`
B. `100%`
C. `300%`
D. can't be determined

Answer

To solve the problem of finding the percentage change when we add 50 to a number \( x \) instead of subtracting 50 from the same number \( x \), we can follow these steps:

### Step 1: Define the two scenarios
1. **Adding 50 to \( x \)**:
\[ n_1 = x + 50 \]

2. **Subtracting 50 from \( x \)**:
\[ n_2 = x - 50 \]

### Step 2: Calculate the difference between the two results
To find the difference between the two results, we subtract \( n_2 \) from \( n_1 \):
\[ \text{Difference} = n_1 - n_2 = (x + 50) - (x - 50) \]

### Step 3: Simplify the difference
Now, simplify the expression:
\[ \text{Difference} = x + 50 - x + 50 = 100 \]

### Step 4: Calculate the percentage change
To find the percentage change, we use the formula:
\[ \text{Percentage Change} = \left( \frac{\text{Difference}}{n_2} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Change} = \left( \frac{100}{x - 50} \right) \times 100 \]

### Step 5: Final expression
Thus, the percentage change can be expressed as:
\[ \text{Percentage Change} = \frac{10000}{x - 50} \]

### Conclusion
Since \( x \) is not specified, we cannot determine a specific numerical value for the percentage change. Therefore, the answer depends on the value of \( x \).