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sister less one-eighth of what remains of the capital after the deduction of the legacy, the computation is this: You consider the heritage as consisting of twelve parts. Each sister receives one-third of what remains of the capital after the subtraction of the legacy; that is, of the capital less the legacy. You perceive that one-eighth of the remainder plus the legacy equals the share of a sister; and also, one-eighth of the remainder is as much as one-eighth of the whole capital less one-eighth of the legacy; and again, one-eighth of the capital less one-eighth of the legacy added to the legacy equals the share of a sister, namely, one-eighth of the capital and seven-eighths of the legacy. The whole capital is therefore equal to three-eighths of the capital plus three and five-eighth times the legacy. Subtract now from the capital three-eighths of the same. There remain. five-eighths of the capital, equal to three and five-eighth times the legacy; and the entire capital is equal to five.and four-fifth times the legacy. Consequently, if you assume the capital to be twenty-nine, the legacy is five, and each sister’s share eight.
Let be the stranger’s legacy.
![{\displaystyle {\begin{aligned}{\tfrac {1}{3}}[1-x]={\text{a sister’s share}}\\{\tfrac {1}{3}}[1-x]-{\tfrac {1}{8}}[1-x]=x\\\therefore \;{\tfrac {5}{24}}[1-x]=x\;\therefore \;{\tfrac {5}{24}}={\tfrac {29}{24}}x\\\therefore \;x={\tfrac {5}{29}}\therefore \;1-x={\tfrac {24}{29}}\\{\text{and a sister’s share}}={\tfrac {8}{29}}\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6770cad71425eec30d4469da5c32908b8fd87eb3)
