Q: How many pages are there in a book if a total of 3209 digits are used for numbering?  

Let p be the total number of pages in the book and d be the number of digits used per page.
We can represent the given information as follows: Number of digits used in 1-digit numbers = 1 * 9 = 9
Number of digits used in 2-digit numbers = 2 * 90 = 180
Number of digits used in 3-digit numbers = 3 * 900 = 2700
Number of digits used in 4-digit numbers = 3209 - (9 + 180 + 2700) = 320
Number of pages with 4-digit numbers = 320 / 4 = 80
Total number of pages = p = 1079
This can be written as a system of equations as follows:
1 * 9 + 2 * 90 + 3 * 900 + (p - 9 - 180 - 2700) * 4 = 3209
(p - 9 - 180 - 2700) / 4 = 80
p = 1079
Solving this system of equations will confirm that the given information is consistent.