Geometric prices

Bob will buy a book if and only if:

  1. The price of the book is an integer number of cents, and ranges from $1.00\$1.00 to $9.99\$9.99, inclusive.

  2. The three digits in the price of the book in order form a geometric progression with a positive common ratio.

If Bob goes to a store with a single book of every possible monetary value, how many books will he buy?

Details and assumptions

For example, Bob will buy a book with price $1.24\$1.24, but not one with price $3.00\$3.00.


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