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

by : Problem $2$

 * De Viro Ambulante in Via: A Walker
 * 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?

Solution

 * $36$.

Proof
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.