Question

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

doubledouble

your money.​ There's one small thing though. Each time I pay​ you, you must give me

​$5656

back for the privilege of​ jumping." Josh​ agreed, jumped the​ fence, received his payment from Sam​ Slick, and paid Sam

​$5656.

Repeating the routine

22

more

timess​,

Josh was distressed to find

thatcomma on the last jump comma, on the last jump,

after Sam had made his payment to​ Josh, Josh had only

​$5656

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

44

times before running out of money. How much money did Josh start with this​ time?

Answer 1

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