Question

Miko has a vast collection of books in her library. English books make up

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:

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

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

$Total = 168$