Dan sold half of his comic books and then bought 8 more. He now has 12. How many did he begin with?

Let's say Dan started out with b comic books.

He sold half of the, leaving (1/2) b books.

He then bought 8 more, so that he owned (1/2) b + 8 books, or 12 books.

Solve for b: Subtract 8 books from both sides, obtaining (1/2) b = 4 books.

Multiplying both sides by 2, to clear the fraction, we get b = 8 books.

Dan started out with 8 books.

He sold half, leaving himself with 4 books.

Then he bought 8 more. 4 plus 8 is 12, which checks with the problem statement.