In a school of $1025$ students, $400$ of them ($\frac{1}{5}$ of the boys and $\frac{4}{7}$ of the girls) cannot swim. How many boys are there? Not sure how to set up an equation for this problem.

A school has $1025$ students. A total of $400$ students cannot swim. This consists of $\frac{1}{5}$ of the boys and $\frac{4}{7}$ of the girls. If $x$ boys can swim, write an equation for $x$ and solve it. How many boys are there in the school?

The answer is the following equation:
$$625-x=\frac{3}{4}\left(400-\frac{x}{4}\right)$$
I understand that $625-x$ represents the number of girls who can swim but I cannot wrap my head around how the $\frac{3}{4}(400-\frac{x}{4})$ came about. Initially I thought that $400-\frac{x}{4}$ must mean the number of girls who cannot swim but if that was the case, the equation should be $400-\frac{x}{5}$ since $\frac{1}{5}$ of the boys cannot not swim.
If someone can help me to make sense of the equation in the answer, that would be much appreciated!

What the equation is saying is that the number of girls who cannot swim is $3/4$ of the number of girls who can swim. This is true since the fraction of girls who can swim is
$$\frac{3}{7} = \frac{3}{4} \cdot \frac{4}{7}$$
As you observed, $625 - x$ is the number of girls who can swim.  Since $x$ is the number of boys who can swim, $x/4$ is the fraction of boys who cannot swim since
$$\frac{1}{5} = \frac{1}{4} \cdot \frac{4}{5}$$
Hence, the term
$$400 - \frac{x}{4}$$
is the number of girls who cannot swim since there are a total of $400$ students who cannot swim and $x/4$ of those are boys.  Since the number of girls who can swim is $3/4$ of the number of girls who cannot swim, we obtain
$$625 - x = \frac{3}{4}\left(400 - \frac{x}{4}\right)$$
Note: Another way to solve the problem is to let $b$ be the total number of male students and $g$ be the total number of female students.  We are told that there are $1025$ students in the school, so
$$b + g = 1025$$
We are also told that $400$ students cannot swim, including $1/5$ of the boys and $4/7$ of the girls cannot swim, so
$$\frac{1}{5}b + \frac{4}{7}g = 400$$
You can solve that system of equations to determine the number of boys in the school, then multiply the result by $4/5$ to find the number of boys in the school who can swim.  You should find that the two methods yield the same result.
