we know that
the basic recipe for split pea soup serves [tex]8[/tex] people
so
by proportion
Find the amount of ingredients needed to serve [tex]32[/tex] people
[tex]\frac{1}{8} \frac{recipe}{people}=\frac{x}{32} \frac{recipe}{people}\\\\8*x=32\\\\x=32/8\\\\x=4\ recipes[/tex]
Mutiply the ingredients by [tex]4[/tex]
dried split peas; [tex](4)*2\frac{1}{4}\ c=9\ c[/tex]
water; [tex](4)*2qt=8qt[/tex]
chopped onion; [tex](4)*\frac{3}{4}c=3c[/tex]
chopped celery; [tex](4)*1c=4c[/tex]
ham shank [tex](4)*2lb=8lb[/tex]