We are given in the question that:
[tex]\frac{1}{4}\text{ gallon}=\frac{2}{3}\text{ bin}[/tex]We are meant to calculate the number of gallons that will fill the entire bin, such that we can have:
[tex]x\text{ gallons}=1\text{ bin}[/tex]We know that the ratio of both expressions will give the same value, therefore, the equation that can be used to solve will be:
[tex]\frac{\frac{1}{4}}{\frac{2}{3}}=\frac{x}{1}[/tex]We can further solve to get the amount of water by cross-multiplying:
[tex]\begin{gathered} \frac{1}{4}\times1=\frac{2}{3}\times x \\ \frac{1}{4}=\frac{2}{3}x \end{gathered}[/tex]Solving, we have:
[tex]\begin{gathered} 2x\times4=3\times1 \\ 8x=3 \\ x=\frac{3}{8} \end{gathered}[/tex]Therefore, it will take 3/8 gallons to fill the bin.
