You have $10$ and $1 bills in your wallet, but no other denomination of currency. A stranger offers you the following deal. For every $1 you have they will trade you to $10. For every $10 you have they will trade you for $1. After both trades are made you must pay the stranger a $2 fee. You know that you have more $1 than $10 so you agree. After the trades are made and you’ve paid free you find that you have doubled your money. How much money did you start with?