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

by : Problem $4$

 * De Homine et Equis in Campo Pascentibus: Some Horses Grazing
 * 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?

Solution

 * $40$.

Proof
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.