Three men go to a cheap motel, and the desk clerk charges them a sum of $30.00 for the night. The three of them split the cost ten dollars each. Later the manager comes over and tells the desk clerk that he overcharged the men, since the actual cost should have been $25.00. The manager gives the bellboy $5.00 and tells him to give it to the men. The bellboy, however, decides to cheat the men and pockets $2.00, giving each of the men only one dollar.
Now each man has paid $9.00 to stay for the night, and 3 x $9.00 = $27.00. The bellboy has pocketed $2.00. But $27.00 + $2.00 = $29.00. Where is the missing $1.00?
Something is wrong here. Let's change the story a little and assume the bellboy takes all $5.00. Then using the same logic would render:
Now each man has paid $10.00 to stay for the night, and 3 x $10.00 = $30.00. The bellboy has pocketed $5.00. And $30.00 + $5.00 = $35.00. Now $5.00 have come out of nowhere. It seems to be getting worse!
What's wrong in the original story is the equation we use. Here's what it should be.
"What the men pay" should equal "what the hotel gets plus what the bellboy gets". Hence the correct equation is: $30.00 - (3 x $1.00) = $25.00 + $2.00 and we can rewrite that as:
$30.00 - $3.00 - $2.00 = $25.00. We can rewrite that once more to really spell it out:
$27.00 - $2.00 = $25.00. Now it's clearer what went wrong.
We see that the originally used equation was totally wrong. The greatest fault is the loose use of the equals sign. We realize quickly that each man pays $9.00. Then we multiply by 3 and add the bell boy's $2.00 and forget about the hotel's $25.00, and we end up confused.