The ball costs **$0.05** (5 cents).

Here's the check:
- Ball: $0.05
- Bat: $1.05 (which is $1.00 more than the ball)
- Total: $0.05 + $1.05 = $1.10 ✓

This is a classic problem because the intuitive answer ($0.10) is wrong — if the ball cost $0.10, the bat would cost $1.10, and together they'd total $1.20.
