# RE7 | meta/muse-spark-1.1 | run 1

## 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 $0.05 and the bat costs $1.05. The intuitive answer of $0.10 is wrong because it would make the total $1.20, not $1.10.

## Why $0.10 feels right but is wrong

Most people quickly split $1.10 into $1.00 and $0.10. If the ball were $0.10, the bat (costing $1.00 more) would be $1.10. Together they would cost $1.20.

This is the classic Cognitive Reflection Test problem - your fast, intuitive System 1 answer conflicts with the slower, correct System 2 answer.

## The math

Let \( x \) = cost of the ball. Then the bat costs \( x + 1.00 \).

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

So:
- **Ball:** $0.05
- **Bat:** $0.05 + $1.00 = $1.05
- **Total:** $0.05 + $1.05 = $1.10

## Quick check

| Answer | Ball | Bat | Total |
| :--- | :--- | :--- | :--- |
| Intuitive ($0.10) | $0.10 | $1.10 | $1.20 - too high |
| Correct ($0.05) | $0.05 | $1.05 | $1.10 - correct |

Want to try the variations with different totals?
