Henry Ernest Dudeney/Modern Puzzles/10 - Unrewarded Labour/Solution

Modern Puzzles by Henry Ernest Dudeney: $10$

A man persuaded Weary Willie, with some difficulty, to try to work on a job for $30$ days at $8$ shillings a day,

on the condition that he would forfeit $10$ shillings a day for every day that he idled.

At the end of the month neither owed the other anything, which entirely convinced Willie of the folly of labour.

Now, can you tell me just how many days' work he put in, and on how many days he idled?

$16 \tfrac 2 3$ days.

Let $d$ be the number of days Willie worked.

We have:

$\ds 8 d$

$=$

$\ds 10 \paren {30 - d}$

$\ds \leadsto \ \ $

$\ds 18 d$

$=$

$\ds 300$

simplifying

$\ds \leadsto \ \ $

$\ds d$

$=$

$\ds \dfrac {300} {18}$

simplifying

$\ds $

$=$

$\ds 16 \tfrac 2 3$

simplifying

$\blacksquare$