5th grade arithmetic approach: there are two dimes per each nickel. Make it a "group", which is 25c, and keep adding up groups until you hit $1 (or just divide 1 by .25). You get four groups, which makes 4 nickels.
8th grade approach: a standard system of two linear equations:
10x + 5y = 100, x = 2y => 20y + 5y = 100, x = 2y => y = 4, x = 8
I would not be able to do this simple math in a stressful and time-limited situation of a TV show, so arithmetic method or test/exclusion as Pathfinder did works better in this case.