Henry Ernest Dudeney/Puzzles and Curious Problems/14 - Horses and Bullocks/Solution

by : $14$

 * Horses and Bullocks
 * A dealer bought a number of horses at $\pounds 17, 4 \shillings$ each,''
 * and a number of bullocks at $\pounds 14, 5 \shillings$ each.
 * He then discovered that the horses had cost him in all $33 \shillings$ more than the bullocks.


 * Now, what is the smallest number of each that he must have bought?

Solution

 * $252$ horses and $327$ bullocks.

Proof
We have that:
 * $\pounds 17, 4 \shillings = 344 \shillings$
 * $\pounds 14, 5 \shillings = 285 \shillings$

Hence we are to find the solution to the Diophantine equation:


 * $344 h - 285 b = 33$

To quote :
 * This is easy enough if you know how, but we cannot go into the matter here.