Math seems pretty straightforward. And it's either simple calculations or complex ones. But there is always a solution...Or is there!!!

Let's try this. (figures are just examples and are not reflective of any rates.)

3 guys who were traveling stopped at a motel for the night. They got a not-so-expensive room for themselves, which cost them $30. So each guy had to shell out $10. This seemed to be a good deal for a stay there.

Just before checking out in the morning, room service came by and told them that the manager had given them a $5 discount. He returned the same to them. The 3 guys each took $1 back and tipped the room service guy with the remaining $2. And off they went headed back home.

Now let's go back and calculate the equation!!!
Each guy 1st spent $10, but took back $1 later. So in the end each spent $9. So 3x9=27. And the room service guy was tipped $2. So 27+2=29.
Hmmmm!!! $29 has been accounted for. So where is that remaining 1 dollar???

Math!!! Simple, but sometimes, complicated, or shall we say, Mind Boggling!!!

There is no 27 + 2; they spent 27: 25 to the hotel, and 2 to the room service guy.

Initially, they spent 3 x 10 for a total of $30, but when they were given back $5, the total spent becomes $25, and the number 30 no longer has any relevance to the calculation. With the $2 tip, the total spent is $27, or $9 each, which equals the initial $10 minus the $1 they each took from the returned $5. So the math works out and there is no remaining dollar.

This is the mistake in your reasoning. The $2 tip is already included in the $27 spent so you can't add it again. They didn't spend $29, they only spent $27: $25 to the hotel and $2 for the tip.