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UKMT Junior Mathematical Olympiad, 2024

Algebra Difficulty 3.0 AMC 10/12 Prove it United Kingdom

My piggy bank contains $x$ pound coins and $y$ pennies and rattles nicely. If instead it contained $y$ pound coins and $x$ pennies, then I would only have half as much money. What is the smallest amount of money my piggy bank could contain?

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