Find mixing ratios to achieve a target concentration.
Alligation is a mathematical method used in pharmacy and chemistry to determine the ratio in which two solutions of different concentrations must be mixed to produce a solution of a desired intermediate concentration. The alligation alternate method uses a simple cross-subtraction: parts of higher = desired - lower, parts of lower = higher - desired. For example, to make 50% alcohol from 90% and 10% solutions: parts of 90% = 50-10 = 40, parts of 10% = 90-50 = 40, giving a 1:1 ratio. This method is extensively used in pharmaceutical compounding for preparing ointments, solutions, and dilutions of specified strength.