Question

15. If the number of professors in a college is P and the number of students is S, and there are 20 times as many students as professors, write an algebraic equation that shows this relationship.

Answer 1

20x + x = P + S
21x = P + S

Answer 2

If there is one professor, there are 20 students.
If there are two professors, there are 40 students.
If there are five professors, there are 100 students.
...
If there are P professors, there must be 20P students.

So the number of students is 20P. So S = 20P.
(Work your way up from easy numbers.)