A library has books on fiction, non-fiction and reference books, 5/9 of all the books in the library are works on fiction and 2/15 are on non-fiction. If there are 7294 reference books, then find the total number of books in the library.
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Fiction = 5/9
Non fiction = 2/15
Therefore reference = subtracting sum of fiction and non fiction from total books
Taking common factors of 9 and 15 as 45
Fiction = 25 /45. (Multiplying 5 to both 5 and 9 in 5/9)
Non fiction = 6/45 (Multiplying 3 to both 2 and 15 in 2/15)
Since the books are in fraction
Total books = 1 (whole books of library)
Non reference books = 1 -(25/45+6/45)
= 1-(31/45)=45-31/45= 14/45 (taking denominator 45 as common for subtraction)
Non reference books = 14/45
Number of Non reference books=7294
Therefore 14/45 of x = 7294
x = 7294*45/14 = 23445
Total no of books in library = 23445
Non fiction = 2/15
Therefore reference = subtracting sum of fiction and non fiction from total books
Taking common factors of 9 and 15 as 45
Fiction = 25 /45. (Multiplying 5 to both 5 and 9 in 5/9)
Non fiction = 6/45 (Multiplying 3 to both 2 and 15 in 2/15)
Since the books are in fraction
Total books = 1 (whole books of library)
Non reference books = 1 -(25/45+6/45)
= 1-(31/45)=45-31/45= 14/45 (taking denominator 45 as common for subtraction)
Non reference books = 14/45
Number of Non reference books=7294
Therefore 14/45 of x = 7294
x = 7294*45/14 = 23445
Total no of books in library = 23445
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