Propositiones ad Acuendos Juvenes/Problems/44 - De Salutatione Pueri ad Patrem

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $44$

A son greeted his father: "Hello Father;"

to which the father replied: "Hello Son.

May you live long, as much as you have lived.

If you triple that number and add one of my years,

you will have lived $100$ years."

How old was the boy at the time?

$16$ years and $6$ months.

Let $x$ years be the age of the boy at the time.

Then we have:

$\ds 3 \paren {x + x} + 1$

$=$

$\ds 100$

$3$ times his age plus his age plus $1$

$\ds \leadsto \ \ $

$\ds 6 x$

$=$

$\ds 99$

simplifying

$\ds \leadsto \ \ $

$\ds x$

$=$

$\ds 16 \tfrac 1 2$

That is, $16$ years and $6$ months.

$\blacksquare$