Tickets for the football game are \$10 for students and \$15 for non-students. If 3000 fans attend and pay \$36250, how many students went?
1. Let \( s \) represent the number of students and \( n \) represent the number of non-students. We are given two equations based on the problem statement:
   \[
   s + n = 3000
   \]
   \[
   10s + 15n = 36250
   \]

2. To eliminate one of the variables, we can manipulate these equations. First, multiply the first equation by 15:
   \[
   15(s + n) = 15 \cdot 3000
   \]
   \[
   15s + 15n = 45000
   \]

3. Now, subtract the second equation from this new equation:
   \[
   15s + 15n - (10s + 15n) = 45000 - 36250
   \]
   \[
   5s = 8750
   \]

4. Solve for \( s \):
   \[
   s = \frac{8750}{5}
   \]
   \[
   s = 1750
   \]

5. Substitute \( s = 1750 \) back into the first equation to find \( n \):
   \[
   1750 + n = 3000
   \]
   \[
   n = 3000 - 1750
   \]
   \[
   n = 1250
   \]

Thus, the number of students who attended the game is \( \boxed{1750} \).