Question

The ratio of the number of fiction books to the number of non-fiction books is 5:2 if there are 1421 book fiction and non-fiction books altogether how many fiction books more than nonfiction books are there in the library

Answer 1

Explanation:

If the ratio of fiction and non-fiction books are 5:2. Therefore that means that the total books were divided into 7 parts and the fiction books took 5 parts while the non-fiction books took two parts.

To get the number of fiction and non-fiction books we first add the ratio

`5 + 2 = 7`

So that means that 7 = 1421

After adding the ratio we now take

The total parts that the books took as the numerator and the total of the ratio as the denominator, and multiply the fraction by the total number of books which is 1421

`(5)/(7) * 1421 = number \: of \: fiction \: books`

`(2)/(7) * 1421 = number \: of \: non - fiction \: books`

let's work out each fraction separately

`(5)/(7) * 1421 = (7105)/(7)`

`(7105)/(7) = 1015`

1015 = Number of fiction books

`(2)/(7) * 1421 = (2842)/(7)`

`(2842)/(7) = 406`

406 = number of non-fiction books

To get the answer to the question we subtract the number of non-fiction books from the number of fiction books

`1015 - 406 = 609`

Answer:

609

Answer 2

306

Explanation:

Let's call the number of fiction books "f" and the number of non-fiction books "n". From the given information, we know that the ratio of fiction books to non-fiction books is 5:2 and the total number of books is 1421, so we can write the following equation:

f + n = 1421

Since the ratio of fiction books to non-fiction books is 5:2, we can write:

f/n = 5/2

We can cross-multiply to solve for f:

f = (5/2) * n

Substituting this expression for f into the first equation:

(5/2) * n + n = 1421

Expanding the left side:

(5/2 + 2/2) * n = 1421

Simplifying the left side:

(5 + 2)/2 * n = 1421

(7/2) * n = 1421

Dividing both sides by (7/2):

n = 1421 * 2/7

n = 204

So there are 204 non-fiction books and 5/2 * 204 = 204 * 5/2 = 102 * 5 = 510 fiction books.

The difference between the number of fiction books and non-fiction books is 510 - 204 = 306. So there are 306 more fiction books than non-fiction books in the library.