Carlos is ten years older than Jose. Five years ago Carlos was three times as old as Jose. How old?

If c is Carlos' age and j is Jose's age, then we can write out the two things we know algebraically.

c = j + 10
c - 5 = 3 * (j - 5)

In the second equation we can replace c with j + 10, or replace j with c - 10 to get an equation in just one term. If we want to know Carlos' age, we should replace j with c - 10. This leaves:

c - 5 = 3 * (c - 10 - 5)
c - 5 = 3c - 45
c = 3c - 40
40 = 2c
c = 20

Carlos is now 20 and Jose is 10. Five years ago they were 15 and 5 (he was three times the age).