I'd start by converting all concentrations to M (=mol/L).
You can do this easily as the question states that you may assume all solutions have density 1 g/mL.
You can express the question in terms of two simultaneous equations:
V1M1 + V2M2 = V3M3 (1)
V1 + V2 = V3 (2)
V# = Volume of solution #
M# = Molarity of solution #
We will call the 1 M solution "solution 1", the 0.2 m solution "solution 2" and the 5% solution "solution 3".
We already know V3, that's 100 mL (= 0.1 L), and M1, that's 1 M.
So to solve the equations we need to:
1. Calculate the molarity M2 - ie. convert 0.2 mol/Kg into mol/L [hint: assuming density of all solutions is 1 g/mL]
2. Calculate M3. [hint: you have already worked out that there is 5 g acetic acid in 100 mL of solution 3 - convert this information into M (=mol/L)]
3. Now the only unknowns are V1 and V2. Two unknowns in two simultaneous equations (1) and (2), solve these equations for V1 and V2 and your homework is done.