Let weight of dried Apples = A oz.
then weight of raisins = 10-A oz.
total cost of 10 oz. of mix
0.38A+0.28(10-A)=10*0.34 =>
Isolate and solve for A
0.10 A=3.40-2.80=0.60
A=0.60/0.10 = 6 oz
hence
weight of dried apples = 6 oz,
weight of raisins = (10-6)=4 oz.