again suggest you take a closer look - the free- built in Solver re excel can handle at least 20 variables simultaneously with a variety of techniques. such that changing any one or two or more can list the effects on all the others. Years ago i used it to find how/what each of a half dozen very loosely related numbers had to be to get a specific set of numbers with a specific total in each of 4 categories- thus proving some book cooking had taken place that the so called auditor missed.
There were at least 6 factorial ( 720 ) times 4 factorial combinations possible, ( about 17, 280 possible ) only one of which was correct. Took me - not a math whiz about an hour to set up after short practice and a few seconds at most to get the answer.