the price has to be less then one dolar

Understanding the Puzzle: The Bat and Ball Problem

The classic bat and ball problem is a well-known puzzle that challenges our intuitive thinking. The problem states: "A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?" Let's break down the solution to this puzzle.

The Common Misconception

Many people quickly assume that the ball costs $0.10. This seems logical at first glance because if the ball is $0.10, then adding $1 for the bat would make the bat $1.10, totaling $1.20. However, this does not match the given total of $1.10 (source).

The Correct Solution

To solve the problem correctly, let's use simple algebra:

1. Let the cost of the ball be ( x ).
2. Then, the cost of the bat is ( x + $1.00 ).
3. The total cost is given as $1.10.

So, the equation becomes:

[ x + (x + 1.00) = 1.10 ]

Simplifying this equation:

[ 2x + 1.00 = 1.10 ]

Subtract $1.00 from both sides:

[ 2x = 0.10 ]

Divide by 2:

[ x = 0.05 ]

Thus, the ball costs $0.05, and the bat costs $1.05. Together, they total $1.10, with the bat being exactly $1 more than the ball (source).

Key Takeaways

• Intuition vs. Calculation: This puzzle highlights how our intuition can lead us astray. The initial assumption of $0.10 for the ball is a common mistake.
• Simple Math: Using basic algebra helps clarify the problem and leads to the correct answer.
• Human Nature: The tendency to overthink or jump to conclusions is a natural part of human problem-solving (source).

Conclusion

The bat and ball problem is a great example of how simple math can challenge our intuitive thinking. By carefully analyzing the problem and using basic algebra, we find that the ball costs $0.05, not $0.10. This exercise serves as a reminder to question our first instincts and rely on logical reasoning.