Four years ago Peter was three times as old as Sylvia, and in 5 years the sum of their ages will be 38 years. Find their present ages.

P = age of Peter and S = Sylvia's age.

We will first decipher "four years prior Peter was three times as old as Sylvia." This can be composed P = 4 + 3 * (S-4).

Next, we interpret "in 5 years the total of their ages will be 38 years" as (P + 5) + (S + 5) = 38.

Presently we have two questions (P and S) and two conditions, so we are prepared to settle. We substitute our first condition for P into our second condition:

(4+3 * (S-4) + 5) + (S+5) = 38

9 + 3S - 12 + S + 5 = 38

2 + 4S = 38

4S = 36

S = 9.

Substitute this once more into the main condition to discover P = 4+3 * (S-4) = 4+3 * (9-4) = 4+15 = 19.