Propositiones ad Acuendos Juvenes/Problems/48 - De Homine qui Obviavit Scolaris

by : Problem $48$

 * De Homine qui Obviavit Scolaris: A Man Meeting some Scholars
 * A man met some scholars and said to them: "How many are there in your school?"
 * One of them answered: "I don't want to tell you that.
 * Count us twice and multiply by $3$.
 * Then divide into $4$ parts.
 * If you add me to this $4$th part, you will have $100$."

Solution

 * $66$.

Proof
Let $x$ be the number of scholars in the school.

Then we have:
 * $\dfrac {3 \paren {x + x} } 4 + 1 = 100$

That is, after algebra:
 * $\dfrac {3 x} 2 = 99$

The result follows.