Given the information, we have a direct proportionality. Then, the proportions would be:
[tex]\frac{7}{x}=\frac{4}{11}[/tex]solving for x we get the following:
[tex]\begin{gathered} \frac{7}{x}=\frac{4}{11} \\ \Rightarrow7=\frac{4}{11}\cdot x \\ \Rightarrow\frac{7}{\frac{4}{11}}=x \\ \Rightarrow x=\frac{11\cdot7}{4}=\frac{77}{4}=19\frac{1}{4} \\ x=19\frac{1}{4} \end{gathered}[/tex]therefore, to paint 11 rooms, we will need 19 1/4 gallons of paint
