In the middle of the school year, $40\%$ of Poolesville magnet students decided to transfer to the Blair magnet, and $5\%$ of the original Blair magnet students transferred to the Poolesville magnet. If the Blair magnet grew from $400$ students to $480$ students, how many students does the Poolesville magnet have after the transferring has occurred?

Let's think step by step and output the final answer within \boxed{}.
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