Age: 10 years ago, the ratio of the ages of a father and son was 7:3. The sum of their present ages is 80 years. Find the father's present age.

Let father’s age = F, son’s age = S 10 years ago: F – 10 and S – 10 So: (F – 10)/(S – 10) = 7/3 → cross-multiplies to: 3(F – 10) = 7(S – 10) → 3F – 30 = 7S – 70 → 3F – 7S = –40

Also: F + S = 80 → F = 80 – S

Substitute: 3(80 – S) – 7S = –40 → 240 – 3S – 7S = –40 → 240 – 10S = –40 → 10S = 280 → S = 28 Then F = 80 – 28 = 52