In school P, the ratio of boys to girls is $7:9$. The difference between the number of boys and girls is $180$. If $65\%$ of the students received scholarships, how many students in school P did **not** get scholarships?

Question

Accepted Answer

**Solution:**

1. Given the ratio of boys to girls is $7:9$, and the difference between boys and girls is $180$.

2. Let the common multiplier be $x$. Then,
   - Number of boys = $7x$
   - Number of girls = $9x$

3. The difference between boys and girls is:
   $$9x - 7x = 2x = 180 \implies x = \frac{180}{2} = 90$$

4. Total number of students in school P:
   $$7x + 9x = 16x = 16 	imes 90 = 1440$$

5. Percentage of students who got scholarships is $65\%$, so those who did not get scholarships are:
   $$100\% - 65\% = 35\%$$

6. Number of students who did not get scholarships:
   $$35\% 	ext{ of } 1440 = \frac{35}{100} 	imes 1440 = 504$$

**Answer:** $504$

Answer

Answer

Answer