2-13. FORMULATING THE EQUATION USING THE MATRIX
a. Example: How many milliliters of water must be added to 300 ml of 70%
alcoholic solution to make a 40% alcoholic solution?
(1) Before the matrix can be formed, the problem has to be analyzed to see
which method is best for working the problem. The key words which indicate that this is
an alligation problem are MUST BE ADDED TO. Other key words indicating alligation
as the best method are MUST BE COMBINED and MUST BE MIXED. In this problem,
40% is the desired strength and must be placed in the center of the matrix. The next
procedure is to see if a higher or lower strength is given. Seventy percent is a higher
strength and must be placed in the upper left-hand corner of the matrix. If no lower
strength is given, it can be assumed to be 0%. The matrix should be as follows:
(2) The relationship of parts of each parts strength to their combined final
volume may be used as the first ratio of a proportion. To formulate the complete
equation, place the known factors in the proper position on the matrix. Assign the X
value first: The question asks, "How many milliliters of water?"; the X value is placed
on the extended line opposite the percentage of alcohol denoted by water.