SOLUTION: (1) A printer uses 2989 digits to number the pages of a large volume book. Determine number of pages of book. (2) If the book has x pages, determine number of pages. Not sur

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Question 1210653: (1) A printer uses 2989 digits to number the pages of a large volume book. Determine number of pages of book.
(2) If the book has x pages, determine number of pages.
Not sure how to solve.
Found 2 solutions by ikleyn, KMST:
Answer by ikleyn(53956)   (Show Source): You can put this solution on YOUR website!
.
1) A printer uses 2989 digits to number the pages of a large volume book. Determine number of pages of book.
(2) If the book has x pages, determine number of pages.
Not sure how to solve.
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(1) First 9 pages from 1 to 9 inclusive use 9 digits.

    so, 2989 - 9 = 2980 digits remain.


(2) Next 90 pages from 10 to 99 inclusive use 2 digits each, or 2*90 = 180 digits, in total.

    So, 2980 - 180 = 2800 digits remain.


(3) Next 900 pages from 100 to 999 inclusive use 3 digits each, or 3*900 = 2700 digits, in total.

    So, 2800 - 2700 = 100 digits remain.


(4) Starting from page 1000, each page requires  four digits.

    So, remaining 100 digits are used for 100/4 = 25 pages.


Thus, 9 + 90 + 900 + 25 = 1024 pages exhaust all  2989 digits, precisely.


ANSWER.  The book has 1024 pages.

Solved.


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Part (1) is a normal Math problem, composed by a professional Math writer/composer.

Part (2) is absurdist composition, written by a person who does not care about what he writes.



Answer by KMST(5404)   (Show Source): You can put this solution on YOUR website!
(1) A printer uses 2989 digits to number the pages of a large volume book. Determine number of pages of book.
The 1-digit numbers are 1 through 9, for a total count of 9,
so for pages 1-9 the printer uses 1 digit character per page for a total of digit characters.
The 2-digit numbers are 10 through 99, for a total count of 99-9=90,
so for pages 10-99 the printer uses 2 digit characters per page for a total of digit characters.
The 3-digit numbers are 100 through 999, for a total count of 999-99=900,
so for pages 100-999 the printer uses 3 digit characters per page for a total of digit characters.
To number pages 1 through 99, the printer has used 9+180+2700=2889 digit characters.
The remaining characters will be used to number pages with 4-digit numbers.
Those 100 digit characters will be enough to number the last pages coming after page 999.
The number on the last page will be .

(2) If the book has x pages, determine number of pages.
Not sure how to solve.
I am not sure how to answer part (2) either.
The obvious answer is if the book has x pages, the number of pages is x.
I cannot even guess what the second question was meant to be.
Maybe what was wanted is the character count needed to number all pages.