The way I started thinking about the problem is, you've got $1.10 to spend in total. $1 is spent on the difference between the bat and the ball. That leaves $.1 which is split evenly between the bat and the ball.

So what I end up doing is, as Tordmor says below:

1.10 - 1 = .10

.10 / 2 = .05

This is essentially the explanation given by wedrifid but I wrote it before reading his and tried to format it more consistently with your comment below.