Question 1110679: Some pages were torn out of a book by mistake. The person repairing the book noticed that the number on one of the facing pages was 11 more than twice the number on their other facing page, and the difference of the page numbers was 23. How many sheeted of paper was torn out of this book?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! WITHOUT A SYSTEM OF EQUATIONS:
Let us open the book at the place where the missing pages were torn off.
Assuming it is an American book (not a Japanese Manga novel),
and you are holding the book as if you were going to read it,
on the left side we see page number  .
= the number on the last not torn page.
Facing that page, on the right side you have page number  ,
"11 more than twice the number on their other facing page."
The difference of the page numbers is
 .
That equation simplifies to  ,
and then to
 and  .
That is good, because when I open an American book,
the page on the left always has an even number.
The page facing page  has a number that is  more.
That number is  .
Pages  and up are still in the book.
Pages 1 through  were in the book originally,
but of those pages, only pages 1 through are still in the book.
The difference is the
 pages missing.
Each sheet has two pages, one on each side, so those  pages
are in the  sheets that were torn out of the book.
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