To find the number of students at the college, we start with the student-to-teacher ratio of 25 to 2. This means that for every 2 teachers, there are 25 students.
Given that there are 174 teachers, we can set up a proportion to find the number of students.
First, calculate how many groups of 2 teachers are in 174 teachers:
\[ \text{Number of groups of 2 teachers} = \frac{174}{2} = 87 \]
Now, since each group of 2 teachers corresponds to 25 students, we can calculate the total number of students:
\[ \text{Number of students} = 87 \times 25 \]
Calculating this gives:
\[ 87 \times 25 = 2175 \]
Thus, the number of students attending the college is
\[ \boxed{2175} \]
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