So, for this problem we know the following:
She +6 dollars, and ended up with 13 total. However, originally she had half of what she has now.
So first what we can do is take away the end total and the six, since she added six more after.
13 - 6 = 7
Since we know she spent half of her original amount, and seven is what she had left after spending it before earning more, we can just double it.
7 * 2 = 14
So, Sara had 14 dollars originally, spent half and gained six to get a total of 13 dollars.
Hope this helped!
- Kat