We are given that 240 miles are driven using 9 gallons of gas. To determine the gallons of gas needed to drive 216 miles we use a rule of three like this:
[tex]\begin{gathered} 240mi\rightarrow9gal \\ 216mi\rightarrow x \end{gathered}[/tex]Now, we cross multiply:
[tex](240mi)x=(216mi)(9gal)[/tex]Now, we divide both sides by 240 mi:
[tex]x=\frac{(216mi)(9gal)}{240mi}[/tex]Now, we solve the operations:
[tex]x=8.1gal[/tex]Therefore, 8.1 gallons are needed.