Question 1158206: 3 people go to stay at a motel and the clerk charges them $30.00 for the room. They split the cost $10 each. Later the manager tells the clerk that he overcharged the guests and that the actual cost should have been $25.00. He gives the clerk $5.00 and tells him to give it to the men. But the clerk decides to cheat them and pockets $2.00. He then gives each guest $1.00. Now each person has paid $9.00 to stay in the room and 3*$9.00=$27.00. The clerk pocketed $2.00. $27.00+$2.00=$29.00. So where is the other $1.00?
Found 2 solutions by ikleyn, VFBundy:
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website! .
With such problems, you should make performance on a stage (or on TV, or in YouTube) as a comic,
but do not send them to the forum.
Answer by VFBundy(438)  (Show Source):
You can put this solution on YOUR website! There is a double-counting of the $2.00 that the clerk pocketed. So, it's not that $1.00 is missing; it's that $2.00 is double-counted.
The total amount paid by the men is $27.00. They paid $25.00 to the hotel and $2.00 to the clerk. The way the problem is presented is that it says they paid $27.00, but then it also says the clerk received $2.00. They are double-counting the $2.00.
Total paid by the men = $27.00 ($25.00 to the hotel; $2.00 to the clerk).
But, then the $2.00 is accounted for AGAIN (double-counted) when the problem mentions that $2.00 was taken by the clerk.
The $27.00 paid by the men INCLUDES the $2.00 paid (stolen) from the clerk. $27.00 is the real amount in play. (Not $30.00, and certainly not $29.00.)
But then, the problem mentions the $2.00 taken by the clerk, and tacks it onto the $27.00 to make $29.00. (The problem is, this $2.00 was ALREADY INCLUDED in the $27.00.)
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