Question 1161769
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Tutor @ikleyn has shown a perfectly good formal algebraic solution to the problem.<br>
If formal algebra is not required, here is a quick and easy informal path to the solution.<br>
(1) The difference between their ages is now (and always will be) 73-31 = 42 years.<br>
(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.<br>
(3) Since their ages are now 31 and 73, that was 10 years ago.<br>
ANSWER: 10 years ago<br>