A local gaming club has more than 2 but fewer than 20 members. Every member of the group purchased a signed copy of the latest book from the legendary Dumas, for a grand total of $299. If each member paid the same whole dollar amount, how many members are in the club?

The number of members of the group must be a whole number, and each member paid the same whole dollar amount. Altogether they paid $299, so both the number of members and the price of the book must be factors of 299.

The factors of 299 are: 1, 13, 23, 299.

The only factor greater than 2 but less than 20 is 13, so that's the number of members. Each of them paid 299:13=23 dollars.

There are 13 members in the club.