#### Answer

There are 3875 male students at the university.
There are 3100 female students at the university.

#### Work Step by Step

Let X represent the number of male students.
Because there are 6975 students at the university, the number of female students is 6975 - X.
The ratio of male students to female students is 5 to 4, or $\frac{5}{4}$.
Now, let’s set up a proportion with the ratio given and a ratio which compares the number of male students to the number of female students.
So, $\frac{5}{4}$ = $\frac{X}{6975 - X}$
To solve this equation, we equate the cross products.
5 $\times$ (6975 - X) = 4 $\times$ X
34875 - 5X = 4X
34875 = 9X
Divide both sides by 9.
X = 3875
There are 3875 male students at the university.
There are 6975 - 3875 = 3100 female students at the university.