Jennifer was going to sell all of her stamp collection to buy a video game. after selling half of them she changed her mind. she then bought fifteen more. how many did she start with if she now has 43?

Alright, we just need to reverse some operations done unto 43. Subtract the 15 from her collection.

43 - 15 = 28.

Sold half? Times half.
28 * 2 = 56

Make sure it works:

56 - 28 = 28. 28 + 15 = 43.

She had 56 cards to start with.

The answer is 10 bud