Question

A library has books on friction ,non friction and references books 5/9of all the books are on friction and 2/15are of non friction. If there are 7294 are references books, how many books are there in the library?

Answer 1

Total number of books in the library = 23,445

Step-by-step explanation:

We are given that a library has books on friction, non friction and references books. 5/9 of all the books are on friction and 2/15 are of non friction.

Also, there are 7294 are references books and we have to find total books in the library.

Let  $x$ = Total number of books in the library

Firstly, as we know that there are only three books in the library ; fiction, non-fiction and references books which means that Sum of number of all these three book will be equal to total number of books in the library.

No. of fiction books + No. of non-fiction books + No. of references books = Total no. of books in the library

So, according to the question;

                         $\frac{5}{9} \times x + \frac{2}{15} \times x + 7294=x$

                          $\frac{5x}{9} + \frac{2x}{15} + 7294=x$

                           $x-\frac{5x}{9} - \frac{2x}{15} = 7294$

Now, we will take the LCM of denominator to make the denominator same of all fractions;

                            $\frac{45x-25x-6x}{45} = 7294$

                               $\frac{14x}{45} = 7294$

                             $14x = 7294\times 45$

                              $14x = 328230$

                               $x=\frac{328230}{14}$ = 23,445

Therefore, there are total 23,445 books in the library.