The sum of the ages of a father and son is 56. Four years ago the father was 3 times as old as the son. Find the present age of each.

Let the father's current age be \( F \) and the son's current age be \( S \). We have two equations based on the problem statements: 1. \( F + S = 56 \) (the sum of their ages) 2. \( F - 4 = 3(S - 4) \) (the father's age four years ago was three times the son's age four years ago) From the first equation, we can express the father's age in terms of the son's age: \( F = 56 - S \). Now, substituting this into the second equation: \( (56 - S) - 4 = 3(S - 4) \). This simplifies to: \( 52 - S = 3S - 12 \). Adding \( S \) to both sides gives us: \( 52 = 4S - 12 \). Adding 12 to both sides results in: \( 64 = 4S \). Dividing both sides by 4, we find: \( S = 16 \). Now, we substitute \( S = 16 \) back into the first equation to find the father's age: \( F + 16 = 56 \), so \( F = 56 - 16 = 40 \). Thus, the present ages are: the father is 40 years old and the son is 16 years old.