Find a number such that the ratio of `(5)/(2)` to the number is the same as the ratio of the number to `(5)/(8)`.

Answer

To solve the problem, we need to find a number \( x \) such that the ratio of \( \frac{5}{2} \) to \( x \) is the same as the ratio of \( x \) to \( \frac{5}{8} \).

### Step-by-step Solution:

1. **Set up the equation based on the given ratios**:
We can express the relationship mathematically as:
\[ \frac{\frac{5}{2}}{x} = \frac{x}{\frac{5}{8}} \]

2. **Cross-multiply to eliminate the fractions**:
Cross-multiplying gives us:
\[ \frac{5}{2} \cdot \frac{5}{8} = x \cdot x \]
This simplifies to:
\[ \frac{25}{16} = x^2 \]

3. **Solve for \( x^2 \)**:
Now we have:
\[ x^2 = \frac{25}{16} \]

4. **Take the square root of both sides**:
Taking the square root gives us:
\[ x = \pm \sqrt{\frac{25}{16}} \]
This simplifies to:
\[ x = \pm \frac{5}{4} \]

5. **Conclusion**:
The possible values for \( x \) are:
\[ x = \frac{5}{4} \quad \text{or} \quad x = -\frac{5}{4} \]