Propositiones ad Acuendos Juvenes/Problems/2 - De Viro Ambulante in Via

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $2$

A man walking down the road saw others coming towards him, and he said to them,

"I wish there were others with you, as many as you are,

plus a quarter of the sum that would be,

plus half of that last amount.

Then with me there would be $100$ altogether."

How many did he see on the road?

$36$.

Let $x$ be the number seen on the road.

Then we have:

$x + x + \dfrac {x + x} 4 + \dfrac 1 2 \paren {\dfrac {x + x} 4} + 1 = 100$

That is, after algebra:

$\dfrac {11 x} 4 = 99$

Hence the result.

$\blacksquare$