You have 200 fish in a bowl such that 99% are guppies.
How many guppies must you remove from the bowl so that 98% of the fish in the bowl are guppies?
How many guppies must you remove from the bowl so that 50% of the fish in the bowl are guppies?
Source: MathCounts News, Winter 1999, p. 1
Hint: Replicate the problem by counting out pennies (guppies) and non-guppies (nickels).
Or, try guess-and-check.
Be prepared for surprises...perhaps even a "duh! moment."
Solution Commentary: In the original bowl, how many fish are not guppies? (2)
Now set up a proportion: 98/100 = (# guppies remaining)/(#guppies remaining + 2).
You should get an answer of "remove 100 guppies," which is counterintuitive.
Many other solution approaches are viable [e.g. setting up and graphing the function f(x) = x/(x+2)], but all lead to the same unsettling surprise.
As closure, you might ask students how this relates to baseball player's batting averages in the early part of the season and near the end of the season.