Three people are eating at a restaurant. The waiter gives them the bill, which totals up to $30. The three people decide to share the expense equally ($10 each), rather than figure out how much each really owes. The waiter gives the bill and the $30 to the manager, who sees that they have been overcharged. The real amount should be $25. He gives the waiter five $1 bills to return to the customers, with the restaurant's apologies. But, the waiter is a dishonest man. He puts $2 in his pocket, and returns $3 to the customers. Now, each of the three customers has paid $9, for a total of $27. Add the $2 that the waiter has stolen, and you get $29. But, the original bill was $30. What happened to the missing dollar?
The answer is that there is no missing dollar. Adding $27 and $2 (to get $29) is the wrong operation. They paid $27, $2 went to the dishonest waiter, and $25 went to the restaurant. You have to subtract $27 minus $2 to get $25. There never was a $29; it has nothing to do with anything.
The numbers in the above puzzle are chosen carefully, to make the wrong answer come very close to the original $30. What if we choose other numbers? The customers paid $30. The manager sees that their bill should be $20. He gives the waiter $10. The waiter pockets $1, and gives $9 to the customers. Each customer has now paid $7, for a total of $21. Add that $21 to the waiter's $1, and you get $22. Where is the missing $8? You would now respond, "You're joking. What does $22 have to do with anything?" And there would be no mystery.