Joan sold half of her comic books and then bought 9 more. she now has 16. how many did she begin with?

That's easy. We know she has 16. She got 16 by buying 9, so first we subtract 9. That leaves us with 7. We also know that's HALF of what she started with, so we will multiply 7 by 2, which gives us 14. That means she started with 14 comic books.