SOLUTION: a mathematics professor is 3 less than 3 times the average age of his students. the difference between the professor's age and the average student is 35 years. find the ages?

Let p = professor's age and s = average of his students age.

Then the first part of the condition says that

p = 3s -3.   (1)

The second part of the condition say that

p - s = 35.  (2)

We need to solve this system (1), (2). 
Express p via s from (2): p = s + 35, and substitute it into (1). You will get

35 + s = 3s -3,   or  2s = 38,  or s = 19.

Then from (1) p = 54.

Answer. The professor's age is 54. Average of his students age is 19.