# Solution

Let me set up equations where:
- b = cost of the ball
- B = cost of the bat

**From the problem:**
- b + B = 1.10
- B = b + 1.00

**Substituting the second equation into the first:**

b + (b + 1.00) = 1.10

2b + 1.00 = 1.10

2b = 0.10

**b = $0.05**

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

To verify: The bat costs $1.05, and $1.05 + $0.05 = $1.10 ✓
