The Bat and Ball

An interesting question that often may catch the average mathematician unaware. Many automatically jump to the conclusion that the ball must cost 10 cents as they subtract $1 from $1.10. However, a ball costing 10 cents is only 90 cents more not $1 more. Therefore upon solving it is found that the ball must cost 5 cents.

Hear is a more visual explanation:

$1.05 - $0.05 = $1

$1.05 + $0.05 = $1.10

Let $a$ be the cost of the bat and $b$ be the cost of the ball. Then we have

$a+b=1.1$ $\color{#D61F06}(1)$

$a=1+b$ $\color{#D61F06}(2)$

So we have,

$1+b+b=1.1$

$2b=1.1-1=0.1$

$b=\$ 0.05$ or $b=5~cents$