Losing weight by doing math, does this sound like it'd work?!

Ok. I am 117 pounds (It may not sound like much but I can feel the difference from the past couple of months) And I want to be about 110. I looked up online and it said that my body NATURALLY burns about 1300 calories per day(My BMR). So if I eat about 1200 calories per day, I have naturally burned 100 calories. I also go to the gym and burn about 400 calories (which adds up to 500 calories burned a day.) And since 3,000 calories = a pound, It would take me about 6 days to burn a pound. Does this sound correct to you? Am I missing something?