$n_X=\frac{17,8-13,4}{23-1}=0,2 mol\Rightarrow \overline{M}=67\Rightarrow X:\begin{cases}CH_3COOH:x mol \\ C_2H_5COOH:y mol \end{cases} $$\Rightarrow \begin{cases}x+y=0,2 \\ 60x+74y=13,4 \end{cases}\Rightarrow \begin{cases}x=0,1 mol \\ y=0,1 mol \end{cases}\Rightarrow m_{CH_3COOH}=6 gam$