Propositiones ad Acuendos Juvenes/Problems/40 - De Homine et Ovibus in Monte Pascentibus

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $40$

De Homine et Ovibus in Monte Pascentibus: A Man and some Sheep Grazing on the Hillside

A man looked at some sheep grazing on the hillside, and said,

"I wish I had these,

and as many again,

plus half of half that total,

plus half of that last amount;

then, counting myself, I would take $100$ to my home.

How many sheep did he see?

$36$.

Let $x$ be the number of sheep seen.

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.

$\blacksquare$

The alert reader will note that this is numerically identical to Problems $2$: De Viro Ambulante in Via.