SOLUTION: Kaylene was asked to number the pages of a book. when she had numbered the last page, she had counted a total of 822 digits. how many 3- digit numbered pages were there'

Algebra ->  Finance -> SOLUTION: Kaylene was asked to number the pages of a book. when she had numbered the last page, she had counted a total of 822 digits. how many 3- digit numbered pages were there'      Log On


   

Question 1044050: Kaylene was asked to number the pages of a book. when she had numbered the last page, she had counted a total of 822 digits. how many 3- digit numbered pages were there'
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
THE FIFTH GRADER'S SOLUTION:
Pages 1 to 9 are numbered with 1 digit each.
That is 9 digits.
Pages 10 to 99 are the nxt 99-9=90 pages,
and each one of those pages is numbered with 2 digits each.
That amounts to another 2%2A90=180 digits.
Beyond page 99, there are 999-99=900+pages+numbered+with+%7B%7B%7B3 digits each,
which would amount to 3%2A9900=2700 digits.
Clearly, that book has less than 999 pages.
The first 99 pages use 9%2B180=189 digits in their numbering.
The next 822-189=633 digits are found,
3 on each page, in the next couple of hundred pages.
How many pages after page 99 are there?
633%2F3=211 .
If there are 211 pages after page 99 ,
the number on the last page is 211%2B99=highlight%28310%29 .