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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

Respuesta :

CaptnKragg
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,
[tex]56 \div \frac{14}{45} = 180[/tex]
The book is 180 pages.

Answer:

129 pages.

Step-by-step explanation:

Let's call [tex]p[/tex] the total number of pages.

He reads [tex]\frac{2}{15}p[/tex] on Monday. There are 13/15 left.

[tex]\frac{1}{3}p[/tex] on Tuesday. There are 2/3 left.

[tex]\frac{2}{9}p[/tex] on Wednesday. There are 7/9 left.

Now, the remainder would be the difference between [tex]p[/tex] and all pages read at this point

[tex]p-\frac{2}{15}p-\frac{1}{3}p-\frac{2}{9}p=\frac{45p-6p-15p-10p}{45} =\frac{14p}{45}[/tex]

So, 3/4 of this is

[tex]\frac{3}{4} \times \frac{14p}{45}=\frac{42p}{180} =\frac{21p}{90}=\frac{7p}{30}[/tex]

The sum of all pages read is

[tex](\frac{2}{15}+\frac{1}{3}+\frac{2}{9}+\frac{7}{30} )p+10=p\\(\frac{12+30+20+21}{90})p +10=p\\\frac{83}{90}p+10=9\\ 10=p-\frac{83}{90}p\\10=\frac{90p-83p}{90}\\ 900=7p\\p=\frac{900}{7}\\ p \approx 129[/tex]

Therefore, there are around 129 pages.