Ron Is Half As Old As Sam, Who Is Three Times As Old As Ted. The Sum Of Their Ages Is 55. How Old Is Ron?

R + S + T = 55
2R = S
3T = S
By looking at what we have we can see that we have a relation between R & S and T & S.
Solve the 2nd and 3rd equations for R and T.
2R = S
R = S/2

3T = S
T = S/3
Substitute these two into the first equation.
R + S + T = 55
(S/2) + S + (S/3) = 55
Multiply both sides by 6 to take out the fractions.

6S   6S
--- + 6S + ---  = 6 x 55
2   3

3S + 6S + 2S = 330

11S = 330

Divide both sides by 11

11S   330
----- =  ------
11   11

S = 30

Plug this into 3T = S
3T = 30
T = 10
Plug S = 30 into 2R = S
2R = 30
R = 15
Test it in the first equation.
R + S + T = 55
15 + 30 + 10 = 55
15 + 40 = 55
55 = 55 Yep, that works.
Ron is 15.