Solving the Ratio Problem: Fiction vs Non-Fiction Books

This problem involves understanding and applying ratios to find an unknown quantity. We are given the ratio between two types of books in a library and the actual number of one type. Our goal is to find the number of the other type.

Understanding the Ratio

The ratio of fiction books to non-fiction books is given as $4:3$. This means that for every 4 fiction books, there are 3 non-fiction books in the library.

Given Information

• Ratio of Fiction Books : Non-Fiction Books = $4:3$
• Number of Fiction Books = 240
• We need to find the Number of Non-Fiction Books.

Applying the Ratio Concept

Let the number of fiction books be represented by $4x$ and the number of non-fiction books be represented by $3x$, where $x$ is a common multiplier.

We know that the actual number of fiction books is 240. Therefore, we can set up the equation:

$4x = 240$

Calculating the Multiplier ($x$)

To find the value of $x$, we need to isolate $x$ by dividing both sides of the equation by 4:

$x = \frac{240}{4}$

$x = 60$

So, the common multiplier is 60.

Calculating the Number of Non-Fiction Books

Now that we have the value of $x$, we can find the number of non-fiction books. The number of non-fiction books is represented by $3x$.

Number of Non-Fiction Books = $3x$

Substitute the value of $x=60$:

Number of Non-Fiction Books = $3 \times 60$

Number of Non-Fiction Books = $180$

Conclusion

Based on the given ratio of $4:3$ and the 240 fiction books, there are 180 non-fiction books in the school library.