Propositiones ad Acuendos Juvenes/Problems/53 - De Homine Patrefamilias Monasterii XII Monachorum

by : Problem $53$

 * De Homine Patrefamilias Monasterii $\text {XII}$ Monachorum: An Abbot with $12$ Monks
 * An abbot had $12$ monks in his monastery.
 * Calling his steward he gave him $204$ eggs and ordered that he give equal shares to each monk.
 * Thus he ordered that he give:
 * $85$ eggs to the $5$ priests,
 * and $68$ to the $4$ deacons
 * and $51$ to the $3$ readers.
 * How many eggs went to each monk, so that none had too many or too few,
 * but all received equal portions as above?

Solution
$17$.

Proof
Take the $12$th part of $204$.

This $12$th part is $17$, so $204$ is $12$ times $17$ or $17$ times $12$.

Just as $85$ is $5$ times $17$, so is $68$ four times and $51$ three times.

Now $5$ and $4$ and $3$ are $12$.

There are $12$ men.

Again add $85$ and $68$ and $51$ which is $204$.

There are $204$ eggs.

Therefore to each comes $17$ eggs as the $12$th part.