Let's denote the cost of the ball as \( x \).

- The bat costs \( x + 1.00 \).
- The total cost is \( x + (x + 1.00) = 1.10 \).

Now, solve the equation:
\[
x + x + 1.00 = 1.10 \\
2x + 1.00 = 1.10 \\
2x = 0.10 \\
x = 0.05
\]

So, the ball costs **0.05** (5 cents).
