# RE7 | meta/muse-spark-1.1 | run 2

## Prompt

A bat and a ball cost $1.10 together. The bat costs $1.00 more than the ball. How much does the ball cost?

## Response

The ball costs 5 cents and the bat costs $1.05. The common intuitive answer of 10 cents is incorrect because then the total would be $1.20.

## The Solution

Let the ball's cost be \(x\).

Then the bat costs \(x + 1.00\).

Together:
\[ x + (x + 1.00) = 1.10 \]
\[ 2x + 1.00 = 1.10 \]
\[ 2x = 0.10 \]
\[ x = 0.05 \]

So:
- **Ball:** $0.05 / 5 cents
- **Bat:** $1.05

Check: $1.05 - $0.05 = $1.00 more, and $1.05 + $0.05 = $1.10 total.

## Why People Get It Wrong

This is a classic item from the Cognitive Reflection Test. System 1 thinking quickly subtracts $1.00 from $1.10 to get $0.10, but fails to check that if the ball were $0.10, the bat would be $1.10 and the total would be $1.20.

Want to try the other two original bat-and-ball style problems from the test?
