The present ratio of students to teachers at a certain

Let's start by assigning variables to the present number of students and teachers. Let's say the present number of students is S, and the present number of teachers is T.

According to the problem statement, the present ratio of students to teachers is 30 to 1, which means:

S/T = 30/1

We can simplify this by multiplying both sides by T:

S = 30T

Now let's use the second piece of information in the problem statement. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the new ratio of students to teachers would be 25 to 1. This means:

(S + 50)/(T + 5) = 25/1

We can simplify this by multiplying both sides by (T + 5):

S + 50 = 25(T + 5)

Now we can substitute the first equation we found (S = 30T) into this equation:

30T + 50 = 25(T + 5)

Simplifying and solving for T:

30T + 50 = 25T + 125
5T = 75
T = 15

Therefore, the present number of teachers is 15.