Henry Ernest Dudeney/Modern Puzzles/6 - Generous Gifts/Solution

by : $6$

 * Generous Gifts

Solution
$20$ people each received a dole of $6$ shillings.

There is a total available weekly amount of $240$ shillings.

With $5$ fewer people, we have $120$ shillings divided between $15$ people, that is $8$ shillings each.

However, with $4$ more people, we have $120$ shillings divided between $24$ people, that is $5$ shillings each.

Proof
Let $N$ denote the total number of shillings to be disbursed.

Let $m$ denote the number of shillings disbursed per person today.

Let $p$ denote the total number of people who are receiving a donation today.

Then we have: