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:

V_{1}M_{1} + V_{2}M_{2} = V_{3}M_{3} (1)

V_{1} + V_{2} = V_{3} (2)

Where:

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 V_{3}, that's 100 mL (= 0.1 L), and M_{1}, that's 1 M.

So to solve the equations we need to:

1. Calculate the molarity M_{2} - ie. convert 0.2 mol/Kg into mol/L [hint: assuming density of all solutions is 1 g/mL]

2. Calculate M_{3}. [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 V_{1} and V_{2}. Two unknowns in two simultaneous equations (1) and (2), solve these equations for V_{1} and V_{2} and your homework is done.