Propositiones ad Acuendos Juvenes/Problems/46 - De Sacculo ab Homine Invento

by : Problem $46$

 * De Sacculo ab Homine Invento: A Man Finding a Purse
 * A man walking along a road, found a purse containing $2$ talents.
 * Others saw this and said: "Friend, give us a portion of your find."
 * He refused to give any to them.
 * So they set upon him and took the bag from him,
 * and each one took $50$ shillings.
 * Seeing that he could not stop them, he reached out and snatched $50$ shillings for himself.


 * How many men were there?

Solution

 * $216$

Proof
There are $75$ (troy) pounds in a talent.

Apparently, in this context, there are also $72$ gold shillings in a troy pound.

Hence there are $75 \times 72 = 5400$ shillings in a talent.

Let $x$ be the number of men that were there.

Then we have: