## The Bat and Ball Puzzle

A bat and a ball cost £1.10. The bat costs £1.00.
How much does the ball cost?
Many people will say 10 pence (or £0.10).
THIS IS WRONG!
If the ball did cost cos £0.10 then the bat =would cost £0.90 more, as opposed to the £1.00 more given in the question.
Suppose the ball costs £
$x$
.
Then the bat cost £
$1+x$
.
Then
$(1+x)+x=1.10$

$1+2x=1.10 \rightarrow x=\frac{1.1-1}{2}=0.05$

The ball costs
$£0.05$
and the bat costs £1.05.