SOLUTION: NINE YEARS AGO, MICHAEL IS FIVE TIMES OLD AS TOM. NOW, HE IS ONLY THREE TIMES AS OLD AS TOM. FIND THEIR PRESENT AGES.

Let T be the Tom's current age.

Then the Michael current age is 3T.


9 years ago Tom was (T-9) years old, while Michael was 3T-9 years old, and for that time

3T -9 = 5*(T-9),   according to the condition.


Simplify and solve for T:


3T - 9 = 5T - 45

45 - 9 = 5T - 3T

36 = 2T  ====>  T =  = 18.


Answer.  Tom is 18 years old;  Michael is 3*18 = 54 years old.


         Nine years ago:  T = 9;  M = 45;  The ratio is   = 5  ----> the solution is correct !