Of the 1500 books in the library, there are 6 times as many books in the fiction section as are in the nonfiction section. Also, there are 700 more books in the reference section than are in the nonfiction section. How many books are in each section?


Let's define the variables for the number of books in each section:

- Let \( x \) be the number of books in the nonfiction section.
- Then, the number of books in the fiction section is \( 6x \) (since there are 6 times as many books in the fiction section as in the nonfiction section).
- The number of books in the reference section is \( x + 700 \) (since there are 700 more books in the reference section than in the nonfiction section).

Now, according to the problem, the total number of books in the library is 1500. So, we can write the equation:

\[
x + 6x + (x + 700) = 1500
\]

Simplify this equation:

\[
x + 6x + x + 700 = 1500
\]

\[
8x + 700 = 1500
\]

Subtract 700 from both sides:

\[
8x = 800
\]

Now, divide by 8:

\[
x = 100
\]

Now that we have \( x = 100 \), we can find the number of books in each section:

- Nonfiction section: \( x = 100 \) books.
- Fiction section: \( 6x = 6 \times 100 = 600 \) books.
- Reference section: \( x + 700 = 100 + 700 = 800 \) books.

So, the number of books in each section is:
- Nonfiction: 100 books
- Fiction: 600 books
- Reference: 800 books

Would you like further details or have any other questions?

Here are 5 related questions to expand on this:
1. What if the total number of books in the library increased by 500? How would that affect each section?
2. How many books would be in the fiction section if the ratio between fiction and nonfiction books changed to 4:1?
3. If 10% of the fiction books were moved to the nonfiction section, how many books would each section have?
4. What percentage of the total library does the reference section represent?
5. If an additional 200 reference books were added, how would the total book count change?

**Tip:** When solving word problems, assigning variables to unknowns and forming equations based on the relationships described can help break down the problem systematically.

Of the 1500 books in the library, there are 6 times as many books in the fiction section as are in the nonfiction section. Also, there are 700 more books in the reference section than are in the nonfiction section. How many books are in each section?

Solve a word problem involving the distribution of books in a library with 1500 books. Learn how algebraic equations help determine the number of books in the nonfiction, fiction, and reference sections based on ratios and differences. Suitable for students in Grades 6-8.

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