Here's how to solve this classic word problem:

* **Let 'b' represent the cost of the ball.**
* **Let 't' represent the cost of the bat.**

We know two things:

1. **t + b = 1.10** (The total cost)
2. **t = b + 1.00** (The bat costs 1.00 more than the ball)

Now we can use substitution. Substitute the second equation into the first:

(b + 1.00) + b = 1.10

Combine the 'b' terms:

2b + 1.00 = 1.10

Subtract 1.00 from both sides:

2b = 0.10

Divide by 2:

b = 0.05

**Therefore, the ball costs 0.05 (or 5 cents).**
