Typically, a syringe will contain 10 ml of spore solution. 1 cc (or ml) per jar is sufficient. So, one syringe will do 10 jars, maybe a few less because if the plunger gets stuck, you will accidentally put too much into a jar or 3.
I would look around for a deal on syringe packs (Try the Spore Works), in case something goes wrong more than 1 is a good thing. Also, if you don't use it all you can store the remainder in a cool, dark place for a while. I would guess at least 6 months, but it varies.
Oh, and that tek I posted is just the most frequently mentioned one, especially for beginners. They all lead to essentially the same end result, just that one I posted is good because it goes into detail on the little pitfalls that can lead to failure/make you give up. You can save yourself a lot of trouble and ensure success if you do everything right the first time.