Greek Anthology Book XIV: 49. - Problem

Problem

 * ''Make me a crown weighing sixty, mixing gold and brass, and with them tin and much-wrought iron.
 * Let the gold and bronze together form two-thirds,
 * the gold and tin together three-fourths,
 * and the gold and iron three-fifths.


 * Tell me how much gold you must put in, how much brass, how much tin, and how much iron, so as to make the whole crown weigh sixty .

Solution
Let $g, b, t, i$ be the quantities in of each of gold, brass, tin and iron.

We have:

So the required quantities are:


 * gold: $30 \frac 1 2$


 * brass: $9 \frac 1 2$


 * tin: $14 \frac 1 2$


 * iron: $5 \frac 1 2$.