Propositiones ad Acuendos Juvenes/Problems/4 - De Homine et Equis in Campo Pascentibus
Jump to navigation
Jump to search
Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $4$
- De Homine et Equis in Campo Pascentibus
- Some Horses Grazing
- A man saw some horses at pasture and wished they were his,
- and that there were others with them that were his,
- the same number again,
- plus a quarter of the sum that would result,
- for then he would glory in $100$ horses.
- How many did the man see at pasture?
Solution
- $40$.
Proof
Let $x$ be the number seen at pasture.
Then we have:
- $x + x + \dfrac {x + x} 4 = 100$
That is, after algebra:
- $\dfrac {10 x} 4 = 100$
Hence the result.
$\blacksquare$
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