I need to set up an equation to solve this problem.

Let me define:
- Let x = the cost of the ball (in dollars)
- Then the bat costs x + 1.00 (since it costs $1.00 more than the ball)

The total cost is $1.10, so:
x + (x + 1.00) = 1.10

Solving:
2x + 1.00 = 1.10
2x = 1.10 - 1.00
2x = 0.10
x = 0.05

Therefore:
- The ball costs $0.05 (5 cents)
- The bat costs $0.05 + $1.00 = $1.05

Let me verify: $0.05 + $1.05 = $1.10 ✓ and $1.05 - $0.05 = $1.00 ✓

The ball costs 5 cents.
