536 Puzzles: Problem & Solution #2: Dollar and Cents

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• 536 Puzzles and Curious Problems

A man entered a store and spent one-half of the money that was in his pocket. When he came out he found that he had just as many cents as he had dollars when he went in and half as many dollars as he had cents when he went in. How much money did he have on him when he entered?

 where a is dollars and b is cents

 now since 99 & 98 are relatively prime and there is no offset the solution is 

Thus he entered the shop with $99.98