I need to set up equations based on the given information.

Let me define:
- b = cost of the ball
- t = cost of the bat

From the problem, I know:
1) b + t = 1.10 (total cost)
2) t = b + 1.00 (bat costs $1.00 more than the ball)

Now I'll substitute equation 2 into equation 1:
b + (b + 1.00) = 1.10
2b + 1.00 = 1.10
2b = 0.10
b = 0.05

Let me verify this answer:
- Ball costs: $0.05
- Bat costs: $0.05 + $1.00 = $1.05
- Total: $0.05 + $1.05 = $1.10 ✓
- Difference: $1.05 - $0.05 = $1.00 ✓

The ball costs $0.05 (5 cents).
