# Bat and ball maths problem

## The problem

In a toy shop there are bats and balls for sale total cost of a bat and a ball is $1.10. If the bat cost $1 more than the ball, how much does the ball cost.

## The typical answer

The typical answer that most people give is $0.10 which is incorrect because:

If the ball cost $0.10 and the bat is $1 more than the ball, therefore the bat cost $1.10 and the ball at 10 cents meaning a total value of $1.20 when it should be $1.10

## The correct answer

The correct answer is 5 cents. Putting 5 cents in to the above statement, the ball cost 5 cents, the bat cost $1 more than the ball so it would cost $1.05. The adding the bat and ball $1.05 + $0.05 = $1.10.

## Why most people get it wrong

It all in the wording. The statement is “if the bat cost $1 **MORE** than the ball”. But most people ignore the word “more” and assume the bat cost $1.

## How to work out the correct answer

You could just sequentially take amounts for the cost of the ball, starting from zero and increment them by one cent and try then against the statement.

Or you could work it out mathematically. The only figures you are explicitly give are 1 and 1.1. But ther is one other figure that is not explicitly given. That is the number of items for sale. 2, A bat and a ball. The formula that gives the correct answer is (1.1-1)/2. That is 1.1 minus 1 and the result divided by 2.