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At a certain university bookstore, all but 5 of its 86 copies of a certain novel currently in stock are hardcover. Every box of copies of this novel that the bookstore orders contains 9 paperback copies and 3 hardcover copies. The store manager intends to order enough boxes to ensure that, after the boxes arrive, three fifths of the copies of the novel in stock are hardcover. Assuming that no copies are sold before the boxes arrive, how many boxes must the manager order?

Let the number of boxes the manager must order be \(n\).

Then, the number of hardbacks that will be in the ordered boxes will be \(3n\), and the total number of books in the boxes will be \(12n\).

After the boxes arrive, the total number of hardbacks will be the following:

\(86 - 5 + 3n\)

After the boxes arrive, the total number of books will be the following:

\(86 + 12n\)

So, we have the following:

\(\frac{81 + 3n}{86 + 12n} = \frac{3}{5}\)

\(\frac{27 + n}{86 + 12n} = \frac{1}{5}\)

\(135 + 5n = 86 + 12n\)

\(7 = n\)

(A) 7
(B) 8
(C) 9
(D) 10
(E) 12


Correct answer: A
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