1. A bank clerk exchanged the euros and cents when cashing a check for a customer, giving cents instead of euros and euros instead of cents. After buying a newspaper for 5 cents, the customer noticed that the remaining value was exactly twice the value of his check. What was the value of the check?
Solution. Let the value of the check be $k$ euros and $y$ cents, where $x$ and $y$ are non-negative integers and $y<100$.
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and this is not possible since $y<100$.

The value of the check was 31 euros and 63 cents.