Propositiones ad Acuendos Juvenes/Problems/16 - De Duobus Hominibus Boves Ducentibus

by : Problem $16$

 * De Duobus Hominibus Boves Ducentibus: Two Men Leading Oxen
 * Two men were leading oxen down the road, and one said to the other:
 * ""Give me two oxen and I'll have as many as you have."
 * Then the other said,
 * "Now you give me two oxen, and I'll have double the number you have."


 * How many oxen were there, and how many did each have?

Solution

 * There were $12$ oxen:
 * The first man had $4$
 * The second man had $8$.

Proof
Let $a$ and $b$ be the number of oxen owned at the start by the first and second man respectively.

It is assumed, by use of the word now in the question, that the suggested transaction actually went ahead, and the $2$ oxen actually changed hands.

We have: