Can you please solve this for me??????

3 people go to a motel. The room is $30. They split it $10 each. While in the room the Mgr. tells the clerk the room was only $25, so he gives her $5 to take back to the 3 people. On the way she cant decide how to split the $5 between the three people so she puts $2 in her pocket and gives them $1 each.....Therefore, the room now only cost the three people $9 each, which is $27 plus the $2 the clerk pocketed,making a total of $29.....Where is the other $1? Can you please help me with this one?

Thanks, Samantha
(Medical Student)

Dear Samantha,

This is a classic problem where the way it is worded is designed to get you thinking in the wrong direction. There is, of course, no missing dollar. Try acting this out with people and money and it becomes clear.

First you would see that the $30 from the people renting the motel room all went to the Manager.

Now track what the manager did with the $30:

$25 he kept for the room

$5 he gave back in change

Now track what happened to the $5 he gave back in change:

$3 the clerk gave back to the renters

$2 she kept for herself

So the $30 is divided as follows: $25 - manager, $2 - clerk, $3 returned to renters.

Another way to see it is to note that the renters spent $27 after receiving the $3 back - the manager got $25 and the clerk kept $2.

Hope this made sense,


Footnote: We have received this question before and you might find Harley's response helpful also. The Centralizer
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