Question

"There came three Dutchmen of my acquaintance to see me, being lately married; they brought their wives with them. The men's names were Hendriek, Claas, and Cornelius; the women's Geertruij, Catriin, and Anna; but I forgot the name of each man's wife. They told me they had been at market to buy hogs; each person bought as many hogs as they gave shillings for one hog; Hendriek bought $23$ hogs more than Catriin; and Claas bought $11$ more than Geertruij; likewise, each man laid out $3$ guineas more than his wife. I desire to know the name of each man's wife".

Answer 1

Let $z$ denote the number of hogs bought by any one of the men, then since $z$ shillings is the price of each hog, $x^2$ shillings represent the value of the hogs bought by this man.

Similarly, is $y^2$shillings be taken to represent the value of the hogs bought by the wife of this man, we have

$x^2-y^2=63$

$(x+y)(x-y)=63$

Factors of $63$;

$1,63;3,21;7,9$;

Therefore,$x=32,12,8$

$\Rightarrow y=31,9,1$

Thus the men bought $32,12,8$ hogs and wife $31,9,1$

Further Hendrick bought $23$ more than Catriin;

Thus Hendrick bought $32$ hogs, and Catriin $9$ hogs; also Class bought $11$ more than Geertruij; then Class bought $12$ and Geertuij $1$ hog.

Hence Cornelius bought $8$ and Anna $31$ hogs,

therefore, Hendrick-Anna, Class-Catriin and Cornelius-Geertuij.