Tyler used 2989 digits to number the pages of a book. How many pages does the book have?
I know that pages 1-9 use 1 digit, total number is 9
Pages 10-99 use 2 digits, total number is 180
Pages 100-999 use 3 digits, 900 pages= 2700
with 25 extra pages
Can you help me from here
pages 1 through 999 need 2889 digits
pages 1000 and up use 4 digit numbers
so 25 pages beyond 999
last page should be 1024
Yes, of course! From the information you provided, we know that pages 1-9 use 1 digit each, totaling 9 digits. Pages 10-99 use 2 digits each, totaling 180 digits. Pages 100-999 use 3 digits each, so that's 900 pages and 2700 digits.
Here's what we can do to find out the total number of pages in the book:
1. Calculate the total number of digits for pages 1-9, 10-99, and 100-999:
- Pages 1-9: 9 digits
- Pages 10-99: 90 pages * 2 digits per page = 180 digits
- Pages 100-999: 900 pages * 3 digits per page = 2700 digits
2. Add up the total digits used for pages 1-9, 10-99, and 100-999:
9 digits + 180 digits + 2700 digits = 2889 digits
3. Now we can calculate how many more digits are needed to reach 2989:
2989 - 2889 = 100 more digits
Since we have 100 more digits available, we can add more pages.
4. Determine how many 4-digit pages we can add with the remaining 100 digits:
- Each 4-digit page uses 4 digits
- Divide the remaining digits by 4 to determine the number of additional pages:
100 digits / 4 digits per page = 25 additional pages
5. Calculate the total number of pages in the book:
- Pages 1-9: 9 pages
- Pages 10-99: 90 pages
- Pages 100-999: 900 pages
- Additional 4-digit pages: 25 pages
9 pages + 90 pages + 900 pages + 25 pages = 1024 pages
Therefore, the book has a total of 1024 pages.