If 500 pounds of mush will feed 20 pigs for a week, for how many days will 200 pounds of mush feed 14 pigs?

Inversely proportional.

$\displaystyle \displaystyle 500\ \times\ \frac{20}{7} = \frac{10 000}{7} $

$\displaystyle \displaystyle = 1428\frac{4}{7} \implies 1428\frac{4}{7}$ pig-days

$\displaystyle \displaystyle 200\ \times\ y\ days = 1428\frac{4}{7}$

$\displaystyle \displaystyle y = \frac{1428\frac{4}{7}}{200} = 7\frac{1}{7}$