Question 1138269
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Let x = # of books at the SECOND shelf; then the number of book at the FIRST shelf is (55-x).


After relocation SECOND shelf has {{{x/2}}} books, while the FIRST shelf has (55-x+ x/2}}} = (55-x/2) books.


The condition says


    {{{4*(x/2)}}} = {{{55 - x/2}}},   or, equivalently,


    2x = {{{55-x/2}}}


Multiply bu 2 both sides, simplify and solve for x


    4x = 110 - x

    4x + x = 110

    5x = 110

    x = 110/5 = 22.


<U>Answer</U>.  22 books at the second shelf and  the rest, (55-22) = 33 at the first shelf.
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Solved.