sonal went to school for 219 days in a full years if her attendance is 75% find the number of days on which the school was open

Answer

To find the total number of days the school was open based on Sonal's attendance, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Sonal attended school for 219 days.
- Her attendance percentage is 75%.

2. **Define the Total Days:**
- Let \( X \) be the total number of days the school was open (which represents 100%).

3. **Set Up the Equation:**
- Since 75% of the total days \( X \) equals the number of days Sonal attended (219 days), we can write the equation:
\[ \frac{75}{100} \times X = 219 \]

4. **Convert the Percentage to a Fraction:**
- We can simplify the equation:
\[ \frac{3}{4} \times X = 219 \]

5. **Solve for \( X \):**
- To isolate \( X \), multiply both sides by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\):
\[ X = 219 \times \frac{4}{3} \]

6. **Calculate \( X \):**
- First, calculate \( 219 \times 4 \):
\[ 219 \times 4 = 876 \]
- Now divide by 3:
\[ X = \frac{876}{3} = 292 \]

7. **Conclusion:**
- Therefore, the total number of days the school was open is \( 292 \).

### Final Answer:
The school was open for **292 days**.

---