a direct variation means, the value of the dependent variable,
varies based on the independent variable times some constant,
let us call it "k", so y=kx, whatever k is
so [tex]\begin{array}{cccccclllll}
\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
\\ \quad \\
&& y={{ (k) }}x
\end{array}[/tex]
[tex]\textit{we know for 15 gallons(x), the price(y) is 17.55}
\begin{cases}
x=15\\
y=17.55
\end{cases}
\\ \quad \\
y=(k)x\implies 17.55=(k)15
\\ \quad \\
\textit{we know for 18 gallons(x), the price(y) is 21.06}
\begin{cases}
x=18\\
y=21.06
\end{cases}
\\ \quad \\
y=(k)x\implies 21.06=(k)18
\\ \quad \\
\textit{what is "k"? or constant of variation, solve either above for "k"}[/tex]
once you get what "k" is, plug it back in the original y=(k)x
then, how many gallons can be purchased with 23.40? namely
if y=23.40, what's "x"? put the "k" value found and solve for "x"
