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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?
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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 = = 2500.
Thus, originally there were 2500 books in the library.
Of them, the number of fiction books was 0.4*2500 = 1000; ANSWER to question b)
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. ANSWER to question a)
Solved.
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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.