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[Seamas]

I had this simple mathematical exchange at a cafe some months ago and I still haven't set it to rights in my brain.  I'm surely overlooking something painfully obvious but I don't know what it is.  Perhaps one of you can help me:

Okay, so I'm at this cafe (it's in Chile), and I have a coffee which costs 900 chilean pesos.  And when I'm finished, I pass the counter girl two 500 peso bills and a moment later I receive my change, a 100 peso coin.

Feeling happy with the service and pleasantly buzzed on caffeine, I decide to tip.  I leave the 100 peso coin on the bar and I leave.  So between 900 for the coffee and 100 in tip, I've paid the cafe 1000 pesos, correct?

Then why have I parted with 1100 pesos in total? 

Edit: Thankyou Urist for pointing out this extremely basic math for my edification.  I was making this more complicated than it really was.  Mental bowel movement is now completed.

[Urist Imiknorris]

You didn't. You paid 1000, got 100 back, and paid the 100 again. You paid 1000 - 100 + 100 = 1000 pesos.

[Levi]

I guess you could argue that you did indeed part with 1100 pesos.  You parted with 1000, then you parted with 100. 


You happened to receive 100 pesos as well, but not the same ones you parted with.   

[Darvi]

Actually, he did part with the same peso that he received.