Simple? math question...
Out of context: Reply #3
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- jonatne0
The $3 amount that has been returned to the guests is a reduction in the amount that the guests paid, so it should be subtracted from the total. The bellhop returned $3 ($1 each), making their total payment $27 (mathematically, $30 - $3). Note that the $3 is subtracted from the total. If the bellhop then changed his mind and returned the additional $2 to the guests, it would also be subtracted from the total. The mistake is made in trying to add this $2 instead of subtracting it. Simple math demonstrates what readers intuitively sense, that there is no missing money. The sum of their payments is $25 in the till, $2 in the bellhop's pocket (totaling $27), plus the $3 in change that the guests now have, which brings the total up to $30.
The incorrect solution is: ($10 - $1) x 3 + $2 = $29. This equation is not meaningful: the number 29 is not significant to the problem, i.e. there is no "missing $1".
The correct solution is: ($10 - $1) x 3 - $2 = $25. In this case the solution is the bill amount, which is also the amount of money left in the till.
In other words, $27 is the amount that the guests have paid. Of that $27, $25 went into the till and $2 went to the bellhop. The other $3 is returned to the guests.