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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?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
Answer by ikleyn(52782)  (Show Source):
You can put this solution on YOUR website! .
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.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
40% of the total number of books were fiction; when the 875 books were borrowed, the number of fiction books left was half the original number. So the fiction books that were borrowed were 20% of the total number of books in the library.
Since 40% of the books were fiction, 60% were non-fiction. When the 875 books were borrowed, the number of non-fiction books decreased by 25%. 25% of 60% is 15%, so the non-fiction books that were borrowed were 15% of the total number of books in the library.
So the 875 books that were borrowed were 20%+15% = 35% of the total number of books in the library.
Let x be the total number of books in the library. Then
.35x = 875
x = 875/.35 = 2500
a) The number of non-fiction books that were borrowed was 15% of the total of 2500:
ANSWER: .15(2500)= 375
b) The number of fiction books in the library at first was 40% of the total of 2500:
ANSWER: .40(2500) = 1000
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