I agree with phat - do the numbers, @40min per day = 4 cartridges. I can easily use up a cartridge in 2 days bcause I drink hot drinks. Some people are extremely miserly with themselves and their fuel and can make it last 4 time longer.

The question is - what are YOUR fuel needs, and you do not know, The kicker is how cold out it is, the efficiency of your pot/windscreen, and your needs. When it gets colder you need MORE fuel to cook anything and you may feel like lots of warm drinks. Maybe you will carry a bit less clothing because you have fuel. Its a very complex equation and you need to work it out for yourself. In the mean time take extra until you know. Its not really that horrible to carry out 2 unused cartridges, better than learning on the second to last day that you are out of fuel. And of course boiling can sterilse your water eliminating the need for filtration or other weighty/energy consuming method. It also depends on your cooking method. Do you want to boil a cup of water and reconstitute some food powder, or do you cook real food? Generally better eating is energy consuming.
Jim