Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages

[math_celebrity]

Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages.

Let r be Richard's age. And a be Alvin's age. We have:

1. r = 3a
2. a + r = 52

Substitute (1) into (2)
a + 3a = 52

Group like terms:
4a = 52

Typing this into the search engine, we get a = 13.

This means Richard is 3(13) = 39