Propositiones ad Acuendos Juvenes/Problems/37 - De Quodam Homine Volenti Aedificare Domum

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $37$

A man wanting to build a house contracted with $6$ builders,

$5$ of whom were master builders.

and the $6$th an apprentice,

to build it for him.

He agreed to pay them a total of $25$ pence a day,

the apprentice to get half the rate of a master builder.

How much did each receive a day?

Each of the master builders earns $4 \frac 6 {11}$ pence per day.

The apprentice earns $2 \frac 3 {11}$ pence per day.

Let $x$ pence denote the amount one master builder earns in one day.

Then we have:

$\ds 5 x + \dfrac x 2$

$=$

$\ds 25$

$\ds \leadsto \ \ $

$\ds x$

$=$

$\ds \dfrac {2 \times 25} {11}$

simplifying

$\ds $

$=$

$\ds 4 \tfrac 6 {11}$

It follows that the apprentice earns half that, that is $2 \frac 3 {11}$ pence, per day.

$\blacksquare$