This is a problem that illustrates how solving equations using algebra can get a solution that may defy a false mathematical intuition.
Since the bat costs $1 more than the ball, and the two of them together cost $1.10, we would like to know the cost of the ball. We can set up an algebraic problem to solve this. Usually we let a variable represent what we are looking for.
Let x be the cost of the ball.
Then setup an equation that combines all the information given:
`x+(x+1)=1.10` since the ball plus the bat cost $1.10. Now simplify the left side.
`x+x+1=1.1` multiply by 10 to get rid of decimals
`10x+10x+10=11` collect like terms
`20x=11-10` simplify the right side
`x=1/20` express as money
The ball costs 5 cents.