Henry Ernest Dudeney/Puzzles and Curious Problems/19 - A Poultry Poser/Solution

by : $19$

 * A Poultry Poser

Solution
A chicken costs $2 \shillings$, a duck costs $4 \shillings$ and a goose costs $5 \shillings$

Proof
Let $c$, $d$ and $g$ be the price in shillings for one chicken, one duck and one goose respectively.

We have:

It follows that $g$ is a multiple of $5$.

If $g \ge 10$ we have from $(2)$ that $c + 2 d < 0$ which cannot happen.

Hence $g = 5$ and so: