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Jaxson and his children went into a grocery store and where they sell bananas for $0.90 each and mangos for $0.50 each. Jaxson has $9.10 to spend and must buy at least 11 bananas and mangos altogether. If Jaxson decided to buy 6 bananas, determine the maximum number of mangos that he could buy. If there are no possible solutions, submit an empty answer.