Emily reads a story book. o the first day, she reads 1/9 of the whole book, and on the second day, she reads 24 pages. The ratio

Question

Natasha_Volkova [10]

3 years ago

15

Emily reads a story book. o the first day, she reads 1/9 of the whole book, and on the second day, she reads 24 pages. The ratio

of the number of pages read to the remaining pages in the two days is 1:4. How many pages are there in this book

Mathematics

2 answers:

Marina86 [1] · Answer 1 · 2023-01-09T22:51:06+03:00

There are 270 pages in this book.

Given that,

Emily reads a storybook the first day,

She reads 1/9 of the whole book, and on the second day, she reads 24 pages.

The ratio of the number of pages read to the remaining pages in the two days is 1:4.

We have to find

How many pages are there in this book?

According to the question,

Let, P is the number of pages,

The first day Emily reads p/9 pages of the whole book,

And the second day she read 24 pages.

The ratio of the number of pages read to the remaining pages in the two days = 1;4 = p/5.

Therefore,

The number of pages reads first day + the number of pages read the second day = The ratio of the number of pages read to the remaining pages in the two days

$\rm \dfrac{p}{9} + 24 = \dfrac{p}{5}\\\\ \dfrac{p}{5} - \dfrac{p}{9} = 24\\\\\dfrac{p \times 9 - p\times 5}{45} = 24\\\\ \dfrac{9p-5p}{45} = 24\\\\\dfrac{4p}{45} = 24\\\\4p = 24\times 45\\\\4p = 1080\\\\p = \dfrac{1080}{4}\\\\p = 270 \ pages$