Part a). If Sylvia fills 7 glasses, then the amount of lemonade she serves is 7/8 of a gallon
[tex]7\cdot\frac{1}{8}=\frac{7}{8}[/tex]Therefore, the amount of lemonade left in the container will be 33/8 gallons.
[tex]5-\frac{7}{8}=\frac{5}{1}-\frac{7}{8}=\frac{5\cdot8}{1\cdot8}-\frac{7}{8}=\frac{40}{8}-\frac{7}{8}=\frac{40-7}{8}=\frac{33}{8}[/tex]Part b). If Sylvia fills 20 glasses, then the amount of lemonade she serves is 5/2 gallons
[tex]\begin{gathered} 20\cdot\frac{1}{8}=\frac{20}{8} \\ \text{Simplifying} \\ \frac{20}{8}=\frac{5\cdot4}{2\cdot4}=\frac{5}{2} \end{gathered}[/tex]Therefore, the amount of lemonade left in the container will be 5/2 gallons
[tex]5-\frac{5}{2}=\frac{5}{1}-\frac{5}{2}=\frac{5\cdot2}{1\cdot2}-\frac{5}{2}=\frac{10}{2}-\frac{5}{2}=\frac{10-5}{2}=\frac{5}{2}[/tex]Part c). If Sylvia fills 32 glasses, then the amount of lemonade she serves is 4 gallons
[tex]32\cdot\frac{1}{8}=\frac{32}{8}=4[/tex]Now, the amount of lemonade left in the container will be 1 gallon
[tex]5-4=1[/tex]