20% of the books in a library are fiction. and the rest are non fiction. When 30% of the fiction books and 15% of the non fiction books are borrowed there are 1,312 books left in the library. How many books are borrowed?
If there are x books, then
f = 0.2x
n = 0.8x
x - 0.30f - 0.15n = 1312
so, now find x, and then figure out how many are borrowed.
To determine how many books are borrowed, we first need to find out the total number of books in the library.
Let's assume the total number of books in the library is "x".
Since 20% of the books are fiction, we can calculate the number of fiction books as 20% of x, which is (20/100) * x = 0.2x.
The rest of the books, which are non-fiction, will be (100% - 20%) = 80% of x. Therefore, the number of non-fiction books is (80/100) * x = 0.8x.
Now, let's calculate the number of borrowed books.
30% of the fiction books are borrowed, which is (30/100) * 0.2x = 0.06x.
15% of the non-fiction books are borrowed, which is (15/100) * 0.8x = 0.12x.
The total number of borrowed books will be the sum of borrowed fiction and borrowed non-fiction books. So, the total number of borrowed books is 0.06x + 0.12x = 0.18x.
We know that there are 1,312 books left in the library. Therefore, the equation becomes:
x - (0.18x) = 1,312.
Simplifying the equation:
0.82x = 1,312.
Dividing both sides by 0.82:
x = 1,600.
Therefore, there are initially 1,600 books in the library.
To find out how many books are borrowed, we substitute this value back into the equation:
0.18x = 0.18 * 1,600 = 288.
Thus, there are 288 books borrowed.