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 1,148 books left in the library. How many books are borrowed?

Answer 1

total number of books in library ---- x

fiction = .2x
non-fiction= .8x

30% of fiction were borrowed, leaving (.7)(.2x) fiction books
15% of non-fiction were borrowed, leaving (.85)(.8x) non-fiction books

(.7)(.2x) + (.85)(.8x) = 1132
.14x + .68x = 1132
.82x = 1132
x = 1132/.82 = 1380.48 ( I was expecting a whole number)
There were 1380 books and 1132 were left, which means
that 1380-1132 or 248 were borrowed

check:
if there were 1380 books
then 276 were fiction and 1104 were nonfiction
30 % of 276 or 83 fiction are out, leaving 193 fiction
15% of 1104 or 166 non-fiction books are out, leaving 938 non-fiction books

sum of remaining books = 193 + 938 = 1131
sum of books borrowed = 83 + 166 = 249

Had I carried decimals in my check calculations, which would be silly since we can't have partial books, the result would have been accurate. The way it is, there seems to be a flaw in the data

Answer 2

Good question 😉