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Algebra Difficulty 2.0 Junior Find the answer United Kingdom

Ali is arranging the books on his bookshelves. He puts half his books on the bottom shelf and two-thirds of what remains on the second shelf. Finally he splits the rest of his books over the other two shelves so that the third shelf contains four more books than the top shelf. There are three books on the top shelf. How many books are on the bottom shelf?

(A) $60$ (B) $50$ (C) $40$ (D) $30$ (E) $20$

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