Another way
x = original # raisins she has
x-1 = after eating one
1/2 (x-1) = how many after giving half away
(1/2 (x-1))-1 = after she eats another one (WHO eats ONE raisin at a time??? LOL)
2/3 (1/2 (x-1))-1) = how many she has left after giving 1/3 away = 6
So: 2/3 (1/2 (x-1))-1) = 6 Solve for 'x' x = 21