30% of a number is 75. Find the number .

Answer

To solve the problem "30% of a number is 75. Find the number," we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find a number (let's call it \( x \)) such that 30% of \( x \) equals 75.

2. **Set Up the Equation**: We can express the problem mathematically as:
\[ 30\% \text{ of } x = 75 \]
This can be rewritten using the percentage as a fraction:
\[ \frac{30}{100} \times x = 75 \]

3. **Simplify the Equation**: To eliminate the fraction, we can rewrite the equation:
\[ \frac{30}{100}x = 75 \]
This can be simplified to:
\[ \frac{3}{10}x = 75 \]

4. **Isolate \( x \)**: To find \( x \), we can multiply both sides of the equation by the reciprocal of \(\frac{3}{10}\), which is \(\frac{10}{3}\):
\[ x = 75 \times \frac{10}{3} \]

5. **Calculate \( x \)**: Now we perform the multiplication:
\[ x = \frac{750}{3} = 250 \]

6. **Conclusion**: The number we are looking for is:
\[ x = 250 \]

7. **Verification**: To ensure our answer is correct, we can check if 30% of 250 equals 75:
\[ 30\% \text{ of } 250 = \frac{30}{100} \times 250 = 75 \]
Since this is true, our solution is verified.

### Final Answer:
The number is **250**.

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