if the number queenie ate is q and the number champ ate is c then q + c = 13 (together they ate 13) and 1+2q = c (champ ate 1 more than 2x what queenie ate)
we know c is 1+2q so you can put that in the other equation where c goes q+c = 13 turns to q+ 1+2q = 13 solve that for q: 3q +1 = 13 3q = 12 q = 4 Queenie ate 4 treats