Of the 1300 books in the library, there are 2 times as many books in the fiction section as are in the nonfiction section. Also, there are 600 more books in the reference section than are in the nonfiction section. How many books are in each section?
Let F be the number of books in the fiction section.
There are 2F books in the fiction section.
There are F/2 books in the nonfiction section.
There are F/2 + 600 books in the reference section.
There are F + F/2 + F/2 + 600 = 1300 books in total.
Combining like terms, we get 2F + 600 = 1300
Subtracting 600 from both sides, we get 2F = 700
Dividing both sides by 2, we get F = 350 books.
There are 350 books in the fiction section.
There are 350/2 = <<350/2=175>>175 books in the nonfiction section.
There are 175 + 600 = <<175+600=775>>775 books in the reference section. Answer: \boxed{350, 175, 775}.
Let's represent the number of books in the nonfiction section as x.
According to the given information, the fiction section has 2 times as many books as the nonfiction section. Therefore, the number of books in the fiction section is 2x.
The reference section has 600 more books than the nonfiction section. Hence, the number of books in the reference section is x + 600.
To find the total number of books in the library, we sum up the number of books in each section:
Total = Nonfiction + Fiction + Reference
1300 = x + 2x + (x + 600)
Simplifying the equation:
1300 = 4x + 600
Subtracting 600 from both sides:
700 = 4x
Dividing by 4:
x = 175
So, there are 175 books in the nonfiction section, 2x = 2 * 175 = 350 books in the fiction section, and x + 600 = 175 + 600 = 775 books in the reference section.