20% of the books in a library were fiction books while the rest were non-fiction books. When 30% of the fiction books and 15% of the non-fiction books were borrowed, there were 1312 books left in the library. How many books were borrowed?

(Please show me your workings clearly.)

X books in Lib.

Fiction = 0.2x books.
Non-fiction = 0.8x. books.

0.7(0.2x) + 0.85(0.8x) = 1312.
0.14x + 0.68x = 1312
0.82x = 1312
X = 1600.

0.2x = 320.
0.8x = 1280.

Books Borrowed = 1600 - 1312 = 288.

Well, it seems like the books in this library have quite the interesting story to tell. Let's dig into the numbers and see what we can discover!

First, let's assume the total number of books in the library is represented by "x."

We know that 20% of the books were fiction books, which means the remaining 80% must be non-fiction books. So, the number of fiction books can be calculated as 0.2 * x.

The number of non-fiction books can be calculated by subtracting the fiction books from the total number of books: 0.8 * x.

Now, we are told that 30% of the fiction books were borrowed, which means 70% of the fiction books were left in the library. Similarly, 15% of the non-fiction books were borrowed, leaving 85% in the library.

Let's take those percentages and calculate the number of books remaining in each category:

Fiction books remaining = 0.7 * 0.2 * x
Non-fiction books remaining = 0.85 * 0.8 * x

The total number of books remaining can be found by adding these two values:

0.7 * 0.2 * x + 0.85 * 0.8 * x = 1312

Let's simplify this equation:

0.14x + 0.68x = 1312

0.82x = 1312

Dividing both sides by 0.82:

x ≈ 1600

So, the total number of books in the library is 1600.

Now, to find out how many books were borrowed, we need to subtract the number of books remaining from the total number of books:

Total books borrowed = 1600 - 1312
Total books borrowed = 288

Therefore, a total of 288 books were borrowed from the library.

Let's denote the total number of books in the library as "x".

Given that 20% of the books were fiction books, we can calculate the number of fiction books as 0.2x.
The rest, which are non-fiction books, would be the remaining 80% or 0.8x.

Now, we know that when 30% of the fiction books were borrowed, it means that 70% (100% - 30%) of the fiction books were left in the library. Similarly, when 15% of the non-fiction books were borrowed, it means that 85% (100% - 15%) of the non-fiction books were left.

So, the number of fiction books left in the library is 0.7 * 0.2x = 0.14x.
And the number of non-fiction books left in the library is 0.85 * 0.8x = 0.68x.

The total number of books left in the library is the sum of the fiction and non-fiction books left:
0.14x + 0.68x = 1312.

Combining like terms, we have:
0.82x = 1312.

To find x, we divide both sides of the equation by 0.82:
x = 1312 / 0.82.

Now, we can calculate the value of x:
x ≈ 1600.

Therefore, the total number of books in the library is approximately 1600.

To find the number of books borrowed, we subtract the number of books left from the total number of books:
1600 - 1312 = 288.

So, 288 books were borrowed.

To solve this problem, we can break it down into steps:

Step 1: Determine the total number of books in the library.
Let's assume the total number of books in the library is "x".

Step 2: Calculate the number of fiction books.
Since 20% of the books in the library were fiction books, we can calculate it using:
Number of fiction books = 20% of x = (20/100) * x = 0.2x

Step 3: Calculate the number of non-fiction books.
The rest of the books in the library, which are non-fiction books, can be calculated using:
Number of non-fiction books = Total number of books - Number of fiction books
Number of non-fiction books = x - 0.2x = 0.8x

Step 4: Calculate the number of borrowed fiction books.
Given that 30% of fiction books were borrowed, we can calculate it using:
Number of borrowed fiction books = 30% of number of fiction books
Number of borrowed fiction books = (30/100) * 0.2x = 0.06x

Step 5: Calculate the number of borrowed non-fiction books.
Given that 15% of non-fiction books were borrowed, we can calculate it using:
Number of borrowed non-fiction books = 15% of number of non-fiction books
Number of borrowed non-fiction books = (15/100) * 0.8x = 0.12x

Step 6: Calculate the total number of borrowed books.
The total number of borrowed books can be calculated by summing the number of borrowed fiction books and the number of borrowed non-fiction books:
Total number of borrowed books = Number of borrowed fiction books + Number of borrowed non-fiction books
Total number of borrowed books = 0.06x + 0.12x = 0.18x

Step 7: Determine the number of books left in the library.
Given that there were 1312 books left in the library, we can set up an equation:
Number of books left = Total number of books - Total number of borrowed books
1312 = x - 0.18x
1312 = 0.82x

Step 8: Solve for x.
To find the value of x, we divide both sides of the equation by 0.82:
x = 1312 / 0.82
x ≈ 1600

Step 9: Calculate the number of borrowed books.
Using the value of x, we can now calculate the number of borrowed books:
Total number of borrowed books = 0.18 * x
Total number of borrowed books = 0.18 * 1600
Total number of borrowed books ≈ 288

Therefore, there were approximately 288 books borrowed from the library.