Propositiones ad Acuendos Juvenes/Problems/37 - De Quodam Homine Volenti Aedificare Domum
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Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $37$
- De Quodam Homine Volenti Aedificare Domum
- A Man Wanting to Build a House
- A man wanting to build a house contracted with $6$ builders,
- $5$ of whom were master builders.
- and the $6$th an apprentice,
- to build it for him.
- He agreed to pay them a total of $25$ pence a day,
- the apprentice to get half the rate of a master builder.
- How much did each receive a day?
Solution
Each of the master builders earns $4 \frac 6 {11}$ pence per day.
The apprentice earns $2 \frac 3 {11}$ pence per day.
Proof
Let $x$ pence denote the amount one master builder earns in one day.
Then we have:
\(\ds 5 x + \dfrac x 2\) | \(=\) | \(\ds 25\) | ||||||||||||
\(\ds \leadsto \ \ \) | \(\ds x\) | \(=\) | \(\ds \dfrac {2 \times 25} {11}\) | simplifying | ||||||||||
\(\ds \) | \(=\) | \(\ds 4 \tfrac 6 {11}\) |
It follows that the apprentice earns half that, that is $2 \frac 3 {11}$ pence, per day.
$\blacksquare$
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