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Algebra Level 2

Charles uses 489 digits to write the page numbers of a book. What is the last page number of the book?


The answer is 199.

Om Agarwal by Om Agarwal , 19, India

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2 solutions

Gabe Smith
Nov 17, 2015

The first 9 pages use 9 digits.

The next 90 pages use 90 × 2 = 180 90 \times 2 = 180 digits.

The next n < 900 n< 900 pages use n × 3 n \times 3 digits.

Thus, we have 9 + 180 + 3 n = 489 9 + 180 + 3n = 489 so 3 n = 399 ⇒ n = 100. 3n = 399 \quad \Rightarrow \quad n = 100.

The total number of pages is 9 + 90 + 100 = 199 . 9+90 + 100 = \boxed{199}.

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please make an edit.....it should be 3n=300 instead of 3n=399

Abhay Lath - 5 years, 6 months ago

good . explanation is very informative

Prasad Imm - 5 years, 6 months ago
Woody Superman
Nov 19, 2015

489 - 9 = 480.

480 - 90x2 = 300.

300 < 900x3 --> the last page only has 3 digits.

300/3 = 100 --> there are 99 + 100 = 199 (pages)

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