Question: A bat and ball cost a combined $1.10. The bat costs one dollar more than the ball. How much does the ball cost? (Reference: Kahneman, pp. 44-45)
Level: Ungraded (can be worked out with ‘trial and error’ approach or with simultaneous equations)
Solution: Careful! The intuitive response is that the ball costs 10 cents. But then this would imply that the bat is $1.00, which does not satisfy the above condition. Here are two methods:
Method 1: Trial & Error
Given that 10 cents won’t work, try some smaller values. Suppose the ball is 5 cents, then the bat must equal: 1.10 – 0.05 = $1.05. This is correct because the difference now between bat and ball is $1. Therefore, the answer to the question is that the ball costs 5 cents.
Method 2: Simultaneous Equations
A more rigorous solution involves representing the above information as two equations. First, let x = cost ($) of the bat, and y = cost ($) of the ball.
① x + y = 1.10
② x – y = 1
We proceed with the elimination method, and we eliminate x, in order to isolate y.
① – ②
y – – y = 2y = 0.1
y = $0.05
∴ The ball costs 5 cents. (Note that this is all that is required to answer the question.)