Only a half of month in the Apartment

Today I got the apartment people to only charage us half of the month of October. When I gave notice on Sept. 10th I gave a 50 days notice that meant we had to get out by Oct. 31st. I had no idea we would find a place in only 10 days.. we don't have that kind of luck, but we did. So now we were stuck paying for rent in October for two places, good thing was that we could take our time moving, bad thing was it was alot of money. So I asked the apartment people if we could only pay half of the month of October and be out by Oct. 14th. I got a reply stating that since we gave notice on Sept. 10 that we could leave by Oct. 1th and only pay for 10 days. I did not like this as I wanted at least two weekends in October to move and I emailed them back asking if we could get an extra five days. They agreed and now we are only paying half of October's rent and we get a full two weeks to move into our new house.