Problem 42385. Combined Ages 4 - Non-symmetric with multiples, n ≥ 3

This problem is slightly more difficult than Combined Ages 3. In this case, some of the sums may include multiples of some individuals' ages. As an example: If the ages of all three individuals with Chris's age added again sum to 98, the ages of Barry (twice) and Chris sum to 84, and the ages of Alex (twice) and Barry sum to 70, what are their individual ages?

The individuals will be represented by the first n capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:

• A+B+C+C = ABCC (= 98)
• B+B+C = BBC (= 84)
• A+A+B = AAB (= 70)

Though the variables are ordered above, they will not always be in the test cases. Write a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.