Let's solve the problem step by step:

Let the **cost of the ball** be **x** dollars.

The **bat costs $1.00 more than the ball**, so the bat costs **x + $1.00**.

**Total cost**:  
Ball + Bat = $1.10  
So:  
x (ball) + (x + $1.00) (bat) = $1.10

Combine terms:  
2x + $1.00 = $1.10

Subtract $1.00 from both sides:  
2x = $0.10

Divide both sides by 2:  
x = $0.05

**Final Answer:**  
**The ball costs $0.05 (5 cents).**
