initially, the dispenser held
[tex]19\frac{1}{4}[/tex]and it dispensed
[tex]12\frac{3}{4}[/tex]the remaining gallons are:
[tex]R=19\frac{1}{4}-12\frac{3}{4}[/tex]Now, let's solve this
[tex]\begin{gathered} R=18\frac{5}{4}-12\frac{3}{4}=(18-12)+(\frac{5}{4}-\frac{3}{4})=6+\frac{2}{4} \\ R=6\frac{1}{2} \end{gathered}[/tex]so the remaining soda is 6+1/2
[tex]6\frac{1}{2}[/tex]