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?

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