Question 1174900
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You have responses showing good formal algebraic solutions, using standard algebraic techniques.  One solution uses a single variable; the other uses two.  That is good; you should know both methods for solving the problem.<br>
If a formal algebraic solution is not required, you can get some good mental exercise (more than by following formal algebraic steps) by solving the problem informally, using logical reasoning and simple mental arithmetic.<br>
Archie is 6 years older than Betty.  (Now; and always).
So when Archie is twice as old as Betty, their ages will be 12 and 6.
Since that will be 2 years from now, their current ages are 10 and 4.<br>
ANSWER: Betty is (now) 4 years old.<br>