Elementary methods in the theory of numbers

Each share is 3a; — 2x — 5, the quantum being 3a;; each recipient of a quantum must return + 2a; + 5 to the fund-box. Out of the fund-box move 6a; pounds to A, and there distribute in 3a;-quanta to 2a; persons, who each return 2x + 5 and therefore a total of 4a; + 10a; to the box as shown. Next move 15a; out of the box to position B and there give.out in 3a; quanta to 5x persons who each return 2x + 5, that is, a total of 10x at C and 25a; at D. Next move out 27a; etc. until the fund is reduced to 45a; -f49 and further quantum distribution is impossible. The quotient is 2a; + 5a; + 9 people and the remainder 45a; + 49 pounds.