Propositiones ad Acuendos Juvenes/Problems/35 - De Obitu Cuiusdam Patrisfamilias

by : Problem $35$

 * De Obitu Cuiusdam Patrisfamilias: A Dying Man's Will
 * A dying man left $960$ shillings and a pregnant wife.
 * He directed that:
 * if a boy is born he should receive $\frac 9 {12}$ of the estate and the mother $\frac 3 {12}$.
 * However if a daughter is born she would receive $\frac 7 {12}$ of the estate and the mother $\frac 5 {12}$.
 * It happened however that twins were born -- a boy and a girl.


 * How much should the mother receive, how much the son, how much the daughter?

Solution
$9$ and $3$ make $12$, and there are $12$ troy ounces to the troy pound.

Similarly, $5$ and $7$ make $12$.

Twice $12$ is $24$.

$24$ (troy) ounces makes $2$ (troy) pounds, that is, $40$ shillings.

Divide $960$ into $24$ parts.

Each part will be $40$ shillings.

Then take $9$ parts of $40$ shillings.

The son receives these $9$ $40$s, which is $18$ pounds, making $360$ shillings.

The mother takes $3$ parts compared to the son and $5$ parts compared to the daughter, and $3$ and $5$ make $8$.

So, take $8$ parts of $40$.

The mother receives $8$ of those $40$s, making $16$ pounds, or $320$ shillings.

Then take what remains, which is $7$ parts, that is $7$ parts of $40$, which is $14$ pounds or $280$ shillings.

This is what the daughter receives.

Adding $360$ and $320$ and $280$ gives $960$ shillings, or $48$ pounds.