QuestionIf there are 240 non-fiction books and the ratio of non-fiction to fiction is 3:7, how many total books are there?

Studdy Solution

STEP 1

Assumptions1. The library has a certain number of non-fiction books and fiction books. . The ratio of non-fiction books to fiction books is37.
3. The number of non-fiction books in the library is240.

STEP 2

First, we need to find the total number of parts in the ratio. We can do this by adding the number of non-fiction books to the number of fiction books in the ratio.
$Total\, parts = Non-fiction\, books\, in\, ratio + Fiction\, books\, in\, ratio$

STEP 3

Now, plug in the given values for the number of non-fiction books and fiction books in the ratio to calculate the total parts.
$Total\, parts =3 +7$

STEP 4

Calculate the total number of parts in the ratio.
$Total\, parts =3 +7 =10$

STEP 5

Now that we have the total number of parts in the ratio, we can find the total number of books in the library. We can do this by dividing the number of non-fiction books in the library by the number of non-fiction books in the ratio, and then multiplying this by the total number of parts in the ratio.
$Total\, books = \left(\frac{Non-fiction\, books\, in\, library}{Non-fiction\, books\, in\, ratio}\right) \times Total\, parts$

STEP 6

Plug in the values for the number of non-fiction books in the library, the number of non-fiction books in the ratio, and the total number of parts in the ratio to calculate the total number of books.
$Total\, books = \left(\frac{240}{3}\right) \times10$

STEP 7

Calculate the total number of books in the library.
$Total\, books = \left(\frac{240}{3}\right) \times10 =800$ There are800 books in the library.

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