original_query: What is alligation and how is it used to solve arithmetic problems related to mixtures of ingredients?
query: What is alligation and how is it used to solve arithmetic problems related to mixtures of ingredients?
answer: Alligation is an old method for solving arithmetic problems involving mixtures.  There are two main types: alligation medial (finding the quantity of a mixture given ingredient quantities) and alligation alternate (finding ingredient amounts to make a mixture of a given quantity).  Alligation medial uses weighted averages, while alligation alternate involves pairing ingredients and adjusting amounts.