The Missing Dollar Problem
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?
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?
Solution:
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.
When we count only real money, the students have $3, the clerk has $2, and the manager has $25. That is $30 total.
Alternate View of the Answer
There is no missing dollar. The students have paid $27 and have kept $3 for themselves and that adds up to $30. Not a real puzzle... just a mistake in math! You cannot tally the clerks total twice, it's already included in the $27 the students have paid. The equation is incorrect...if they paid $27 and the clerk kept $2...then that does not add up to anything.
There is no missing dollar. The students have paid $27 and have kept $3 for themselves and that adds up to $30. Not a real puzzle... just a mistake in math! You cannot tally the clerks total twice, it's already included in the $27 the students have paid. The equation is incorrect...if they paid $27 and the clerk kept $2...then that does not add up to anything.