Hello TheOtherTink,
What a brain teaser! Here is how I went about it...but this still leaves me puzzled, a little bit...
* If the bellhop were honest, he would give $1.66 to each salesman = $5
* Then $10 - $1.66 = $8.33 each salesman paid, and $8.33 x 3 = $25, which is the correct price. And $1.66 x 3 = $5, and $25 + $5 = $30. So as long as we do it that way, everything adds up okay to $30.
* However, the cheated salesmen were paying $9 each, and $9 x 3 = $27, which is $2 over the price, enter the bellhop with his $2 self-tipping, 66¢ x 3 = $2 apx.
* So if you add the bellhop's $2 to the difference between $27 and $30, then $2 + $3 = $5. Then add this $5 to the $25 room rent and you are back at $30 again.
* Do you buy it?