If there were n cookies, then n/7 are oatmeal and 6n/7 are chocolate.
n/11 were burned and 10n/11 were unburned.
So n must be divisible by both 7 and 11, that is, n is a multiple of 77. There are less than 100 cookies so there must be 77 cookies: 11 oatmeal, 66 chocolate, 7 burned, 70 unburned.