Alligations/ Learn
Jason Sparks, Austin Community College
calculator

When to use the alligation process:

  1. When combining two existing products of a given strength/concentration to create a new desired strength/concentration.
  2. When combining a pure product or higher strength product, with a diluent to create a new desired strength/concentration.

How to calculate needed quantities of each ingredient:

To aide in this process, a visual matrix may be used to better facilitate the mathematical process.

The quantity of the higher strength solution is calculated by dividing the number of parts of the higher strength by the total number of parts, then multiplying by the final, required, quantity of the desired product.


Parts of Higher
Strength Needed
Total Number of Parts
X Final Required quantity of desired product = Required Quantity of Higher Strength Product

The quantity of the lower strength solution is calculated by dividing the number of parts of the lower strength by the total parts, then multiplying by the final, required, volume.


Parts of Lower
Strength Needed
Total Number of Parts
X Final Required quantity of desired product = Required Quantity of Lower Strength Product

To check your work, add the calculated required quantities of the higher and lower strength products. If they add to the final required quantity of desired, then you are correct. If not, re-evaluate your work to determine if an error was made.


Required Quantity of Lower Strength Product + Required Quantity of Higher Strength Product = Final Required Quantity of Desired Product

 

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