The Bat and the ball

together bat and ball cost 1 dollar and 10 cents =110 cents

The bat costs a dollar more than the ball. so at first , subtracting 1 $ or 100 cents from 110 cents and it is 10 cents.

so, the ball cost = $\frac {10}{2}$ cents =5 cents

$\text{bat + ball = 110}$ $\color{#D61F06}(1)$

$\text{bat} =100 + \text{ball}$ $\color{#D61F06}(2)$

Substitute $\color{#D61F06}(1)$ in $\color{#D61F06}(2)$ , we have

$100 + \text{ball} + \text{ball} = 110$

$\text{2ball} = 110 - 100$

$\text{2ball} = 10$

$\text{ball} = \boxed{5}$

Suppose cost of a ball = Y
As per given conditions
Ball(cost) + bat(cost) = 110 cent
So (100 + Y) + Y = 110
2Y = 10
Y = 5

Explanation: When you read the math problem, you probably saw that the bat and the ball cost a dollar and ten cents in total and when you processed the new information that the bat is a dollar more than the ball, your brain jumped to the conclusion that the ball was ten cents without actually doing the math. But the mistake there is that when you actually do the math, the difference between $1 and 10 cents is 90 cents, not $1. If you take a moment to actually do the math, the only way for the bat to be a dollar more than the ball AND the total cost to equal $1.10 is for the baseball bat to cost $1.05 and the ball to cost 5 cents.