Tutor @ikleyn has shown a perfectly good formal algebraic solution to the problem.
If formal algebra is not required, here is a quick and easy informal path to the solution.
(1) The difference between their ages is now (and always will be) 73-31 = 42 years.
(2) When Micah was 3 times Alice's age, the difference in their ages was twice Alice's age. (The difference between x and 3x is 2x). Solving, 2x = 42; x = 21; it was when Alice was 21 and Micah was 21+42 = 63 that Micah was 3 times as old as Alice.
(3) Since their ages are now 31 and 73, that was 10 years ago.
