Question 1202746
.
In a library, 40% of the books were fiction and the rest were non-fiction. 
When 875 books were borrowed, the number of fiction books became half of the original number 
and the number of non-fiction books were decreased by 25%.
a) How many non-fiction books were borrowed?
b) How many fiction books were there at first?
~~~~~~~~~~~~~~~~~


<pre>
Let x be the original number of books in the library.

According to the problem's description, there were 0.4x fiction books 
and 0.6x non-fiction books originally (the rest).


When 875 books were borrowed, the number of remaining fiction     books became half of 0.4x, i.e. 0.2x;
                              the number of remaining non-fiction books became 0.75 of 0.6x, i.e. 0.75*0.6x = 0.45x.


So, when 875 were borrowed, the total of remaining books became 0.2x + 0.45x = 0.65x.


Obviously, this amount is equal to x-875, so we have this equation

    0.65x = x - 875.


Simplify and find x

    875 = x - 0.65x

    875 = 0.35x

      x = {{{875/0.35}}} = 2500.


Thus, originally there were 2500 books in the library.

Of them, the number of fiction     books was 0.4*2500 = 1000;    <U>ANSWER to question b)</U>
         the number of non-fiction books was 0.6*2500 = 1500.


The number of non-fiction books borrowed was 25% of 1500, i.e. 0.25*1500 = 375.   <U>ANSWER to question a)</U>
</pre>

Solved.


----------------------


The solution is obtained using one single equation and one single unknown.


It made the setup and the solution extremely simple, short, clear and transparent.