Propositiones ad Acuendos Juvenes/Problems/49 - De Carpentariis
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Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $49$
- De Carpentariis
- Carpenters
- $7$ carpenters made $7$ wheels each.
- How many carts were fitted?
Solution
- $12$, with one wheel left over.
Proof
Let $x$ be the number of carts fitted.
Let $y$ be the number of wheels made.
It is presumed that each cart has $4$ wheels.
Thus we have:
\(\ds x\) | \(=\) | \(\ds \floor {\dfrac y 4}\) | where $\floor {\, \cdot \,}$ denotes the floor function | |||||||||||
\(\ds \) | \(=\) | \(\ds \floor {\dfrac {7 \times 7} 4}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \floor {\dfrac {49} 4}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 12\) |
That is, we have that:
- $49 = 4 \times 12 + 1$
The result follows.
$\blacksquare$
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