Propositiones ad Acuendos Juvenes/Problems/10 - De Linteo

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $10$

De Linteo

A Linen Problem

I have a piece of linen, $60$ cubits long and $40$ cubits wide.

I want to cut it into portions, each of which will be $6$ cubits long and $4$ wide.

How many portions can be made of it?

Solution

$100$.

Proof

We have that:

$6$ goes into $60$ a total of $10$ times

$4$ goes into $40$ also a total of $10$ times.

Thus the cloth can be cut into $10 \times 10 = 100$ pieces that are $6$ cubits long and $4$ cubits wide.

$\blacksquare$

Sources

• c. 800: Alcuin of York: Propositiones ad Acuendos Juvenes ... (previous) ... (next)
• 1992: John Hadley/2 and David Singmaster: Problems to Sharpen the Young (Math. Gazette Vol. 76, no. 475: pp. 102 – 126)  www.jstor.org/stable/3620384