Question

Tyler reads 2/15 of a book on Monday 1/3 of it on Tuesday 2/9 of it on wensday,and 3/4 of the remainder on Thursday, if he still has 14 pages left to read on Friday, how many pages are there in the book

Answer 1

Since Tyler read 3/4 of the remainder, that means 14 pages must be 1/4 of the remainder.

4x14=56 pages

Similarly, 56 pages should be the remainder after he read 2/9 of the book on wednesday.

So, 1-(2/15+1/3+2/9)=14/45

If 56 pages is 14/45 of the whole book,

`56 / (14)/(45) = 180`
The book is 180 pages.

Answer 2

129 pages.

Explanation:

Let's call
`p` the total number of pages.

He reads
`(2)/(15)p` on Monday. There are 13/15 left.

`(1)/(3)p` on Tuesday. There are 2/3 left.

`(2)/(9)p` on Wednesday. There are 7/9 left.

Now, the remainder would be the difference between
`p` and all pages read at this point

`p-(2)/(15)p-(1)/(3)p-(2)/(9)p=(45p-6p-15p-10p)/(45) =(14p)/(45)`

So, 3/4 of this is

`(3)/(4) * (14p)/(45)=(42p)/(180) =(21p)/(90)=(7p)/(30)`

The sum of all pages read is

`((2)/(15)+(1)/(3)+(2)/(9)+(7)/(30) )p+10=p\\((12+30+20+21)/(90))p +10=p\\(83)/(90)p+10=9\\ 10=p-(83)/(90)p\\10=(90p-83p)/(90)\\ 900=7p\\p=(900)/(7)\\ p \approx 129`

Therefore, there are around 129 pages.