Josh wanted to buy a bike but​ didn't have enough money. Sam Slick​ said, "I can fix that. Each time you jump that​ fence, I'll triple your money.​ There's one small thing though. Each time I pay​ you, you must give me ​$54 back for the privilege of​ jumping." Josh​ agreed, jumped the​ fence, received his payment from Sam​ Slick, and paid Sam ​$54. Repeating the routine 1 more time​, Josh was distressed to find that after Sam had made his payment to​ Josh, Josh had only ​$54 with which to pay Sam and so had nothing left.​ Sam, of​ course, went merrily on his​ way, leaving Josh wishing that he had known a little more about mathematics. ​ (a) How much money did Josh have before he made his deal with​ Sam?
​(b) Suppose the problem is the​ same, but this time Josh jumps the fence 3 times before running out of money. How much money did Josh start with this​ time?