Let's solve the problem step by step.

Let \( x \) represent the cost of the ball in dollars. According to the problem, the bat costs $1.00 more than the ball, so the bat costs \( x + 1.00 \).

The total cost of the bat and ball together is $1.10. This can be expressed with the following equation:

\[ x + (x + 1.00) = 1.10 \]

Simplify the equation:

\[ 2x + 1.00 = 1.10 \]

Subtract 1.00 from both sides:

\[ 2x = 0.10 \]

Divide both sides by 2:

\[ x = 0.05 \]

Thus, the ball costs $0.05.
