\(\frac{4x}{7}=\frac{5y}{11}=\frac{4x+5y}{7+11}=\frac{4\left(x+y\right)+y}{18}=\frac{4.79+y}{18}.\)
\(\Rightarrow\frac{5y}{11}=\frac{4.79+y}{18}\Rightarrow90y=4.11.79+11y\)
\(\Rightarrow79y=4.11.79\Rightarrow y=44\)
\(\frac{4x}{7}=\frac{5y}{11}=\frac{5.44}{11}=20\Rightarrow x=35\)