A bat and ball cost $1.10 in total. The bat costs $1 more than the ball. How much is the ball?

Answer & explanation

5 cents

Ten cents feels compelling because $1 plus ten cents equals $1.10, but it ignores the requirement that the bat cost exactly $1 more than the ball. If the ball costs x, then the bat costs x + $1; 2x + $1 = $1.10, so x is five cents. The example illustrates how a fluent intuitive answer can bypass a necessary check.