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If it takes 1074 digits to number the pages of a book starting with page 1. how many pages are in the book? The book has a total of pages. ​

Respuesta :

mhanifa

Answer:

  • 394 pages

Step-by-step explanation:

1- digit numbers:

  • 1 to 9, number of digits = 9

2- digit numbers:

  • 10 to 99, number of digits = 2(99 - 9) = 180

3- digit numbers:

  • 100 to 999, number of digits = 3(999 - 99) = 2700

This is more than we have, but we know the number of pages is 3-digit.

Let it be x, then we have:

  • 9 + 180 + 3(x - 99) = 1074
  • 3(x - 99) = 1074 - 189
  • 3(x - 99) = 885
  • x - 99 = 885/3
  • x - 99 = 295
  • x = 295 + 99
  • x = 394

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