Solve word problems leading to linear equations
Of the 1200 books in the library, there are 3 times as many books in the fiction section as are in the nonfiction section. Also, there are 400 more books in the reference section than are in the nonfiction section. How many books are in each section?
How many books in fiction, books in nonfiction, and books in reference
Let's set up some equations to represent the given information.
Let's say there are x books in the nonfiction section.
According to the problem, there are 3 times as many books in the fiction section as in the nonfiction section. Therefore, the number of books in the fiction section is 3x.
Also, there are 400 more books in the reference section than in the nonfiction section. So, the number of books in the reference section is x + 400.
Now, let's add up the number of books in each section to get the total number of books in the library.
x + 3x + x + 400 = 1200
5x + 400 = 1200
5x = 1200 - 400
5x = 800
x = 800/5
x = 160
So, there are 160 books in the nonfiction section, 3(160) = 480 books in the fiction section, and 160 + 400 = 560 books in the reference section.