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

Propositiones ad Acuendos Juvenes by Alcuin of York: 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.

$\blacksquare$

Sources

• c. 800: Alcuin of York: Propositiones ad Acuendos Juvenes ... (previous) ... (next)
• 1992: John Hadley/2 and David Singmaster: Problems to Sharpen the Young (Math. Gazette Vol. 76, no. 475: pp. 102 – 126)  www.jstor.org/stable/3620384