A.K. Tolpygo

Petya's bank account contains 500 dollars. The bank allows only two types of transactions: withdrawing 300 dollars or adding 198 dollars.

What is the maximum amount Petya can withdraw from his account if he has no other money?

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Since 300 and 198 are divisible by 6, Petya will only be able to withdraw an amount that is a multiple of 6 dollars. The maximum number that is a multiple of 6 and does not exceed $500 is 498.

Let's show how to withdraw 498 dollars. Perform the following operations: $500-300=200, 200+198=398, 398-$ $300=98, 98+198=296, 296+198=494$. The amount in the bank has decreased by 6 dollars.

By repeating this procedure 16 times, Petya will withdraw 96 dollars. Then he can withdraw 300, deposit 198, and withdraw 300 again. As a result, he will have 498 dollars.