Counting Counters (with Mathematical Journeys)

I was reading through the ATM's excellent Mathematical Journeys when I came across this excellent puzzle. But before I go into that a little history...Mathematical Journeys is a compilation of some of the puzzles from the excellent Departure Points series. This set of four books (plus one for primary) were the result of an extended ATM conference session at the 1977 conference. They serve as excellent starting points that let learners (of all ages!) discover and investigate mathematics in all its aspects.

The puzzle to investigate is this:

Leila has a jar of counters, when she counts them into piles of four, she has two left over. When she counts them into piles of five she has one left over. How many counters could she have had?

This is wholesale taken from the Mathematical Journeys I make no denial, but I really like how it encourages working with modulo numbers...when is x (mod 4) = 2 and x (mod 5) = 1? The possibilities to investigate are massive, introducing another count into piles of 6? Changing the two numbers? Giving bounds (more than 10 less than 100?)...a fantastic problem.

Thanks to Greg for spotting the mistake!