x% of x is the same as 10% of

Options

A. `(x)/(10)`
B. `(x^(2))/(10)`
C. `(x^(3))/(10)`
D. `(x)/(100)`

Answer

To solve the problem "x% of x is the same as 10% of which number?", we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Expression**:
- We need to express "x% of x" mathematically.
- This can be written as:
\[ \frac{x}{100} \times x = \frac{x^2}{100} \]

2. **Setting Up the Equation**:
- We know that "10% of some number" can be expressed as:
\[ 10\% \text{ of } y = \frac{10}{100} \times y = \frac{y}{10} \]
- We need to find the value of \( y \) such that:
\[ \frac{x^2}{100} = \frac{y}{10} \]

3. **Cross-Multiplying**:
- To eliminate the fractions, we can cross-multiply:
\[ x^2 \times 10 = y \times 100 \]
- This simplifies to:
\[ 10x^2 = 100y \]

4. **Solving for y**:
- Now, we can solve for \( y \) by dividing both sides by 100:
\[ y = \frac{10x^2}{100} \]
- Simplifying this gives:
\[ y = \frac{x^2}{10} \]

5. **Conclusion**:
- Therefore, the number \( y \) such that "x% of x" is the same as "10% of y" is:
\[ y = \frac{x^2}{10} \]

### Final Answer:
The answer is \( \frac{x^2}{10} \).