Help me solve this pls.

A book is published in 3 volumes, the pages being numbered from 1 on wards. The page numbers are continued from the first volume to the second volume to the third. The number of pages in the second volume is 50 more than that in the first volume, and the number of pages in the third volume is one and a half time that in the second. The sum of the page numbers on the first pages of the three volumes is 1709. If n is the last page number, what is the largest prime factor of n?

#Algebra

Easy Math Editor

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`2 \times 3`	$2 \times 3$
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Comments

Suppose $n_1$ , $n_2$ and $n_3$ are the number of pages in volumes $1$ , $2$ and $3$ of the book, respectively. In the question, it is given that $n_2 = n_1 + 50$

and that

$n_3 = \frac{3}{2} n_2.$

Furthermore, you know that the sum of the first page numbers of each volume can be expressed by

$1 + (n_1+1) + (n_2+1) = n_1+n_2+3 = 1709,$

which simplifies to

$n_1 + n_2 = 1706.$

If $n \equiv n_1 + n_2 + n_3$ , then find $n_1$ , $n_2$ and $n_3$ by solving the system of linear equations that we have obtained. That is as far as I will take you; as you have asked us to help you out, you will need to do the rest of the leg work on your own. I hope this helps you.

A Former Brilliant Member - 2 years, 9 months ago

Thanks a lot! I got the answer.

Harsh Aryan - 2 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$