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In a library, 30% of the books are fiction and the rest are non-fiction. Given that there are 2,000 more non-fiction books than fiction books, what is the total number of books in the library?

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Question:

A
5,000

explanation

Let: x be the number of fiction books in the library

x + 2,000 = the number of nonfiction books

Total number of books = \(x + (x + 2,000)\)

The problem says that 30% of the total number of books are fiction

Therefore: \(\frac{\mathrm{30} }{\mathrm{100}} \times [x+(x+2000)] = x\)

\(\frac{\mathrm{30} }{\mathrm{100}} \times [2x+(2000)] = x\)

\(\frac{\mathrm{60x+60000} }{\mathrm{100} } = x\)

\(60x+60,000=100x\)

\(100x–60x=60,000\)

\(40x=60,000\)

\(x = 1,500\), the number of fiction books

\(x + 2,000 = 1,500 + 2,000 = 3,500\), the number of nonfiction books

\(1,500 + 3,500 = 5,000\), the total number of books in the library

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