Let's see, if we had 10 months we'd need 5 months of 36 days and 5 of 37 days. Each month is a little over 5 weeks, which is 35 days. Maybe 10 months of 35 days and a special month of 15 days.
(I still prefer 13 months of 28 days with 1 extra day, but superstitious people don't like 13.)(I also like my personal idea of 6 day weeks with 4 days working and 2 days off. That leaves 1 odd week of 5 days.)