Let the cost of the ball be \(x\).

Then the bat costs \(x + 1.00\).

Total cost:
\[
x + (x + 1.00) = 1.10
\]
\[
2x + 1.00 = 1.10
\]
\[
2x = 0.10
\]
\[
x = 0.05
\]

The ball costs \$0.05.
