Propositiones ad Acuendos Juvenes/Problems/3 - De Duobus Proficistentibus Visis Ciconiis

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $3$

De Duobus Proficistentibus Visis Ciconiis: Two Travellers and a Flock of Storks

Two walkers saw some storks and wondered how many there were.

Conferring, they decided:

If there were the same number again,

and again,

and then a half and a third of the sum that would make,

plus two more,

that would make $100$.

How many storks were seen?

$28$.

Let $x$ be the of storks seen.

Then we have:

$x + x + x + \dfrac 1 2 \times \dfrac 1 3 \times \paren {x + x + x} + 2 = 100$

That is, after algebra:

$\dfrac {21 x} 6 = 98$

Hence the result.

$\blacksquare$