We can solve this problem by proportional relationships:
[tex]\begin{gathered} \frac{8}{5}=\frac{35}{x} \\ 8x=5\times35 \\ 8x=175 \\ x=\frac{175}{8}=21.875 \end{gathered}[/tex]Rounding to the nearest integer, you are going to need 22 potatoes for all 35 people.