This is from Barron's GRE prep guide.
If 1/2x years ago Adam was 12, and 1/2x years from now he will be 2x years old, how old will he be 3x years from now?
The solution is:
Since 1/2x years ago, Adam was 12, he is now 12 + 1/2x. So 1/2x years from now, he will be 12 + 1/2x +1/2x = 12 + x. But, we are told that at that time he will be 2x years old. So, 12 + x = 2x -----> x = 12. Thus, he is now 12 + 6 = 18, and 3x or 36 years from now he will be 18 + 36 = 54.
I highlighted the 6 in the solution above as I don't know where that comes from. Can anyone help explain the solution a bit further?