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Puzzle: Sally's age is 12 years plus half her age. How old is she?
You should be able to get it by trial and error, even though there are easier ways. By the way, 18 doesn't work. 12+6 is 18. But 6 is not half of 18.
Answer: Algebra is the easy way:
A = 12 + A/2
A/2 = 12 [Subtracting A/2 from both sides]
A = 24
You can also reason it out, without much algebra. Her age is some number plus half her age. Well it must be half her age plus half her age, right? That is the only way to add up to her age. So half her age is 12. And she is 24.
This kind of puzzle comes up fairly often in puzzle books. That is because people often start out wrong, when trying to solve it. So the puzzle seems difficult. But it is easy.
Addendum:
Here is an interesting puzzle:
Puzzle: Billy is twice as old as Sally was when Billy was as old as Sally is now. And the total of their ages is 28. How old are they?
Answer: The difficulty is to go from English to algebra. Here is what I make of that long sentence. Sally is S years old; Billy is B years old. Billy was once S years old. How long ago was that? It was B-S years ago. How old was Sally then? She was S-(B-S) or 2S-B years old then. Billy is now twice that old: B = 2(2S-B) = 4S-2B or 3B = 4S. And we also know that S+B=28. We have two equations and two unknowns, we can probably solve for S and B. Sally is 12 and Billy is 16. By the way, I checked my work.