# The Missing Dollar

Three students checked into a hotel and paid the clerk $30 for a room ($10 each). When the hotel manager returned, he noticed that the clerk had incorrectly charged $30 instead of $25 for the room. The manager told the clerk to return $5 to the students. The clerk, knowing that the students would not be able to divide $5 evenly, decided to keep $2 and to give them only $3.

The students were very happy because they paid only $27 for the room ($9 each). However, if they paid $27 and the clerk kept $2, that adds up to $29. What happened to the other Dollar?

There is a saying that you cannot add apples and oranges. If you have 3 apples and 2 oranges do you have 5 apples? No. Do you have 5 oranges? No. You have five fruits, but the number of apples and oranges has not changed. Similarly, you cannot add real money and “what they think they paid”.

**When we count only real money, the students have $3, the clerk has $2, and the manager has $25. That is $30 total.**

Accounting of Real Money | ||
---|---|---|

Before | After | |

Student #1 | $10.00 | $1.00 |

Student #2 | $10.00 | $1.00 |

Student #3 | $10.00 | $1.00 |

Clerk | $0.00 | $2.00 |

Manager | $0.00 | $25.00 |

Total | $30.00 | $30.00 |

The students were very happy because they paid only $27 for the room ($9 each). However, if they paid $27 and the clerk kept $2, that adds up to $29.

above line is just meant for confusing you

When the total bill is $25 share of each student becomes 8.33 and not 9

Notice in each case, the net amount traded is 27 dollars. Students pay 27, clerk gets 27. When the problem states that the clerk keeps two dollars, THE TWO DOLLARS ARE ALREADY INCLUDED IN THE 27 DOLLARS (25+2). So the last sentence has a trick. The clerk does not keep 2 more dollars on top of the 27. There is supposedly a 1 dollar difference between 29 (27 plus 2) and 30 (30 is the 8 initial amount of money handled but net amount handled is 27; 27 +3 -3). But the 30 is talking about the highest amount of the money exchanged, while 29 is a made up number.

### Your Answer

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