Answer
$$F_{E G} =1128 \frac{k g}{m^{3}}$$
Work Step by Step
$\text{in our case we can apply the law of linearity}$
$\begin{aligned} \rho_{\operatorname{mix}} &=\rho_{H_{2}} O \frac{50 \%}{100 \%}+\rho_{E G} \frac{50 \%}{100 \%} \\ 1064 \frac{k g}{m^{3}} &=1000 \frac{k g}{m^{3}} \cdot 0.5+F_{E G} \frac{k g}{m^{3}} \cdot 0.5 \\ \Longrightarrow & F_{E G}=\frac{1064-500}{0.5} \frac{k g}{m^{3}} \\ F_{E G} &=1128 \frac{k g}{m^{3}} \end{aligned}$
