Let the number of professors be x.
If there are 16 times as many students as professors, then the number of students will be:
[tex]x\times16=16x[/tex]
If the number of students and professors is 42,500, then we have that:
[tex]\begin{gathered} x+16x=42500 \\ 17x=42500 \end{gathered}[/tex]
Solving by dividing both sides by 17, we have:
[tex]\begin{gathered} x=\frac{42500}{17} \\ x=2500 \end{gathered}[/tex]
Hence, we can calculate the number of students in the college to be:
[tex]\Rightarrow2500\times16=40000[/tex]
Therefore, there are 40,000 students in the college.
