Share on Facebook Share on Twitter Email
Answers.com

Alligation

 
Dictionary: Al·li·ga·tion
Home > Library > Literature & Language > Webster 1913

n.

[L. alligatio.]

1. The act of tying together or attaching by some bond, or the state of being attached. [R.]

2. (Arith.) A rule relating to the solution of questions concerning the compounding or mixing of different ingredients, or ingredients of different qualities or values.

Note: The rule is named from the method of connecting together the terms by certain ligature-like signs. Alligation is of two kinds, medial and alternate; medial teaching the method of finding the price or quality of a mixture of several simple ingredients whose prices and qualities are known; alternate, teaching the amount of each of several simple ingredients whose prices or qualities are known, which will be required to make a mixture of given price or quality.

Search unanswered questions...

Enter a question here...
Search: All sources Community Q&A Reference topics

Wikipedia: Alligation
Top
Home > Library > Miscellaneous > Wikipedia
Alligation should not be mistaken for allegation.

Alligation is an old and practical method of solving arithmetic problems related to mixtures of ingredients. There are two types of alligation: alligation medial, used to find the quantity of a mixture given the quantities of its ingredients, and alligation alternate, used to find the amount of each ingredient needed to make a mixture of a given quantity. Alligation medial is merely a matter of finding a weighted mean. Alligation alternate is more complicated and involves organizing the ingredients into high and low pairs which are then traded off.

Contents

Examples

Alligation medial

Suppose you make a cocktail drink combination out of 1/2 Coke, 1/4 Sprite, and 1/4 orange soda. The Coke has 120 grams of sugar per liter, the Sprite has 100 grams of sugar per liter, and the orange soda has 150 grams of sugar per liter. How much sugar does the drink have? This is an example of alligation medial because you want to find the amount of sugar in the mixture given the amounts of sugar in its ingredients. The solution is just to find the weighted average by composition:

{1\over2}\times 120 + {1\over4}\times 100 + {1\over4}\times 150 = 122.5 grams per liter.

Alligation alternate

Suppose you like 1% milk, but you have only 3% whole milk and ½% low fat milk. How much of each should you mix together to make an 8 ounce cup of 1% milk? This is an example of alligation alternate because you want to find the amount of two ingredients to mix together to form a mixture with a given amount of fat. Since there are only two ingredients, there is only one possible way to form a pair. The difference of 3% from the desired 1%, 2%, is assigned to the low fat milk, and the difference of ½% from the desired 1%, ½%, is assigned alternately to the whole milk. The total amount, 8 ounces, is then divided by the sum 2 + {1\over2} = {5\over2} to yield 16/5, and the amounts of the two ingredients are

{16\over5}\times{1\over2} = {8\over5} ounces whole milk and {16\over5}\times2 = {32\over5} ounces low fat milk.

This article incorporates content from the 1728 Cyclopaedia, a publication in the public domain.

External links


This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

 
 

 

Copyrights:

Dictionary. Webster 1913 Dictionary edited by Patrick J. Cassidy  Read more
Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Alligation".  Read more