Need answer to word problem

Question

mike is paid for writing numbers on pages of a book.  since different pages require different numbers of digits. mike is paid for writing each digit . in his last book he wrote 642 digits. how many pages was in the book?

Answer 1

Hi Hodge,

 

Assuming that Mike started with page 1, there are 9 single digits from 1 to 9,

 

there are 90 double digits from 11 to 99 for a total of 180 digits

 

180 + 9 = 189 digits so far.

 

There are 642 - 189 = 453 digits remaining

 

Now we get to the 3 digit numbers

 

Divide 453 by 3 to find how many three digit numbers there are--> 151

 

So there were 251 pages in the book.

 

Dan