Question

Miko has a vast collection of books in her library. English books make up
3
8
of her collection.
5
7
of the remaining books are Chinese books and the rest are German books. How many books are there in her book collection if there are 75 Chinese books?

Answer 1

Answer:

168 books

Step-by-step explanation:

Given

$English = \frac{3}{8}$

$Chinese = \frac{5}{7}$ of the remaining books

Required

Determine the total number of books

If the proportion of the English books is 3/8, the the remaining is:

$Remaining = 1 - English$

$Remaining = 1 - \frac{3}{8}$

Take LCM

$Remaining = \frac{8 - 3}{8}$

$Remaining = \frac{5}{8}$

From the question, we understand that:

$Chinese = \frac{5}{7}$ of the remaining books

This means:

$Chinese = \frac{5}{7} * \frac{5}{8}$

$Chinese = \frac{5*5}{7*8}$

$Chinese = \frac{25}{56}$

From the question, we also understand that 75 are Chinese books.

The total number of books can then be calculated using:

$Chinese = \frac{25}{56} * Total$

Substitute 75 for Chinese

$75 = \frac{25}{56} * Total$

Make Total the subject:

$Total = \frac{56 * 75}{25}$

$Total = \frac{4200}{25}$

$Total = 168$

Answer 2

There are 168 books are there in her book collection if there are 75 Chinese books.

Given

Miko has a vast collection of books in her library.

English books = 3/8

Chinese books = 5/7.

Ratio proportion;

A ratio is a comparison of two or more numbers that indicates their quantities in relation to each other.

The proportion of the English books is 3/8, the remaining is:

$\rm Remaining\ books=1-\dfrac{3}{8}\\ \\ Remaining\ books=\dfrac{8-3}{8}\\\\ Remaining\ books=\dfrac{5}{8}$

Then,

Chines books = ratio of Chinese book × ratio of remaining books × Total books

$\rm 75=\dfrac{5}{7}\times \dfrac{5}{8}\times Total \ books\\\\Total \ books =\dfrac{75 \times 7\times 8}{5\times 5}\\\\Total \ books =3\times 56\\\\Total \ books=168$

Hence, there are 168 books are there in her book collection if there are 75 Chinese books.

To know more about proportion click the link given below.

https://brainly.com/question/12674321