cats get sick from new food

My stepmother was telling me recently that she bought a new catfood that was on sale and had a problem with the cats vomiting after eating it.  My suggestion:  Buy a small bag of the old food and mix the food about half and half- old and new for a few days, then mix a quarter old and three quarters new and so on, gradually switching the food.  And if that food is not on sale again, gradually switch back to the old food again.  Sometimes a sudden change in diet can cause stomach upset in dogs and cats.