Propositiones ad Acuendos Juvenes/Problems/2 - De Viro Ambulante in Via
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Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $2$
- De Viro Ambulante in Via
- A Walker
- A man walking down the road saw others coming towards him, and he said to them,
- "I wish there were others with you, as many as you are,
- plus a quarter of the sum that would be,
- plus half of that last amount.
- Then with me there would be $100$ altogether."
- How many did he see on the road?
Solution
- $36$.
Proof
Let $x$ be the number seen on the road.
Then we have:
- $x + x + \dfrac {x + x} 4 + \dfrac 1 2 \paren {\dfrac {x + x} 4} + 1 = 100$
That is, after algebra:
- $\dfrac {11 x} 4 = 99$
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