Let's solve this step by step:

1) Let's define a variable for the ball's price:
   Let x = price of the ball

2) Given the information about the bat, its price will be (x + 1.00)

3) We know the total cost is 1.10, so we can write an equation:
   x + (x + 1.00) = 1.10

4) Simplify the equation:
   x + x + 1.00 = 1.10
   2x + 1.00 = 1.10

5) Subtract 1.00 from both sides:
   2x = 0.10

6) Divide both sides by 2:
   x = 0.05

7) So the ball costs 0.05 (5 cents)

Let's check:
• Ball costs 0.05
• Bat costs (0.05 + 1.00) = 1.05
• Total: 0.05 + 1.05 = 1.10 ✓
• Bat costs 1.00 more than the ball ✓

The ball costs 0.05 (5 cents).
