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

by : 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?

Solution

 * $28$.

Proof
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.