Jasmine is traveling from the USA to Europe and needs to exchange her US dollars to Euros. She starts with $600. The exchange rate is 1 USD = 0.85 EUR. After exchanging her money, she spends half of her Euros on a hotel and then spends an additional 50 EUR on food. How many Euros does she have left? Let's think step by step and output the final answer within \boxed{}.
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