Question

In numbering pages of a book, a printer used 3289 digits. How many pages were in the book, assuming the first page of the book was number 1? Justify your answer. (b) Find the number of digits the printer will need for a book with n pages, for any positive integer n. Write this function of n as simple a form you can.

Answer 1

The number of the pages in the book if the first page will be numbered as 1 will be 1099 pages. And if the number of the pages is n then the function is shown below.

What is Algebra?

Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.

In numbering pages of a book, a printer used 3289 digits.

Then the number of the pages in the book if the first page will be numbered as 1.

One digit number = 1 - 9 = 9 digits

Two digit number = 10 - 99 = 2 x 90 = 180 digits

Three digit number = 100 - 999 = 3 x 900 = 2700 digits

Then the total number of the digit is used will be

→ 9 + 180 + 2700

→ 2889

The number of the remaining digits will be

→ 3289 - 2889

→ 400

Then the four-digit number will be

→ 400/4

→ 100

Then the total number of the pages will be

Total pages = 9 + 90 + 900 + 100

Total pages = 1099

If n pages are there, then the number of the digits are required will be

$\left\{\begin{matrix}n, & 1\leq n\leq 9 \\9+(n-9)2, & 10\leq n\leq 99 \\189+(n-9)3, & 100\leq n\leq 999 \\. & . \\. & . \\\end{matrix}\right.$

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1