text: The problem misleadingly suggests that the amount the three men paid ($27) and the amount the bellboy kept ($2) SHOULD add up to the original amount ($30).  Not so.  Actually, the $27 INCLUDES the $2.  In other words, of the $30 the three men originally had, $25 went to the motel and $2 went to the bellboy -- that's the $27; the remaining $3 went back to the men.\n\nImagine the same problem with different numbers.  Let's say the clerk discovers he overcharged the men by $27.  He gives the $27 to the bellboy; the bellboy gives each man $1, and keeps $24.  Obviously, the amount the men paid ($27) and the amount the bellboy kept ($24) don't add up to anything significant (and certainly not even close to $30).