Propositiones ad Acuendos Juvenes/Problems/4 - De Homine et Equis in Campo Pascentibus

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $4$

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?

$40$.

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.

$\blacksquare$