起初学校操场上共有 2120 名学生。 在 536 名男生和 $\frac{1}{4}$ 的女生离开后，男生人数与女生人数之比变为 4 : 9。最后操场上的女生比男生多多少人？ 答：___

1. Express the number of girls at first in terms of units

In the end, the ratio of boys to girls is $4 : 9$. Let the number of girls in the end be $9$ units.
Since $\frac{1}{4}$ of the girls left, the remaining girls represent $1 - \frac{1}{4} = \frac{3}{4}$ of the girls at first.
$\frac{3}{4}$ of girls at first = $9$ units
$\frac{1}{4}$ of girls at first = $9 \div 3 = 3$ units
Total girls at first = $3 \times 4 = 12$ units

2. Express the number of boys at first in terms of units

Let the number of boys in the end be $4$ units.
Since $536$ boys left, the number of boys at first = $4$ units $+ 536$.

3. Use the total number of students at first to find the value of 1 unit

Total students at first = Girls at first + Boys at first
$12\text{ units} + 4\text{ units} + 536 = 2120$
$16\text{ units} = 2120 - 536$
$16\text{ units} = 1584$
$1\text{ unit} = 1584 \div 16 = 99$

4. Find the difference between the number of girls and boys in the end

Difference in units in the end = $9\text{ units} - 4\text{ units} = 5\text{ units}$
Difference = $5 \times 99 = 495$