# RE7 | perplexity/sonar-pro | 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 **$0.05 (5 cents)**. Then the bat costs **$1.05**, which is exactly $1.00 more than the ball, and together they sum to $1.10.[1](https://www.psychologicalscience.org/publications/observer/obsonline/a-new-twist-on-a-classic-puzzle.html)[2](https://www.reddit.com/r/confidentlyincorrect/comments/vfqwiz/a_bat_and_a_ball_are_110_and_the_bat_is_1_more/)

## Explanation

Let the **ball cost** be \(x\) dollars.

- The bat costs **$1.00 more** than the ball, so bat = \(x + 1\).[1](https://www.psychologicalscience.org/publications/observer/obsonline/a-new-twist-on-a-classic-puzzle.html)
- Together they cost $1.10, so:
  \[
  x + (x + 1) = 1.10
  \]

Combine like terms:
\[
2x + 1 = 1.10
\]

Subtract 1 from both sides:
\[
2x = 0.10
\]

Divide by 2:
\[
x = 0.05
\]

So the ball costs **$0.05**, and the bat costs \(0.05 + 1 = 1.05\).[2](https://www.reddit.com/r/confidentlyincorrect/comments/vfqwiz/a_bat_and_a_ball_are_110_and_the_bat_is_1_more/)[7](https://sites.math.rutgers.edu/~zeilberg/calc5_2014/p/pAmazings.pdf)

Would you like to see a few similar puzzles that test the same kind of reasoning?
