Henry Ernest Dudeney/Modern Puzzles/10 - Unrewarded Labour

by : $10$

 * Unrewarded Labour
 * 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?

Solution
$16 \tfrac 2 3$ days.

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

We have: