A bat and ball cost $1.10 total; the bat costs $1.00 more than the ball. How much is the ball, and why does this matter on a desk?

How to answer

The ball is $0.05, not $0.10. Let the ball = b; then bat = b + 1.00, so 2b + 1.00 = 1.10 and b = 0.05 (bat = 1.05, total 1.10). If the ball were $0.10 the bat would be $1.10 and the total $1.20. On a desk this matters because the fast intuitive answer is wrong — under time pressure you must verify the math, not trust the gut, before you quote or trade.

Key idea: Blurting '$0.10' — the System-1 answer almost everyone gives before checking the constraint.