How are bequests calculated when three parties (uncle, maternal uncle, grandfather) have bequests defined mutually as a fixed amount minus a fraction of another's bequest?

General Chapter

Al-Mughni

Book of Bequests

Book 31 · Issue 4 · Bab 1

Open in Qurani

Primary text

In cases involving three intertwined bequests defined by mutual subtractions (e.g., Ten minus a quarter of B's bequest), the initial step is to multiply all the denominators of the fractional exclusions together to find the total divisible base (the total amount upon which the division rests). This base is then increased by one to represent the total fixed sum referenced across all bequests. The individual bequest value is calculated by subtracting the appropriate fraction from its corresponding exclusion denominator, multiplying the result by the other two exclusion denominators, multiplying that by the fixed sum (Ten), and then dividing by the total divisible base.

Supporting text

Another approach utilizes algebraic balancing by assigning initial arbitrary units (items/currency) to each legatee and then iteratively equating the resulting quantities after adjusting for the specific subtractions to isolate the true value of one unit.