Tires: Tire Size, winter tires, tire width

Question
My car currently has 215-60R-15 all seasons installed.  When I went to buy winter tires the dealer recommended putting on 205-65R-15 because there is more selection in this tire size.  

I always thought the amount you change the tire width by, you need to alter the aspect ratio by the exact same amount.  Meaning if I go with the narrower tire I have to install the 205-70R-15 (i.e. decrease the width by 10, increase the ratio by 10).

Is that the case or will the 205-65R-15 fit on the car also?

Answer
Alex,

In order to maintain the load carrying capacity going down in width 10 (a single increment) should be compensated by going up in aspect ratio one increment (5).  So you had the idea right, just the details were wrong.

BTW, this does work 100% of the time and in particular doesn't wrong for more than 3 iterations.