Sagaris, the Treasurer of Earsdale had forgotten how many gold, silver and bronze coins were kept in the city vaults. So he decided to ask the three guards, each of whom guarded one type of coin, how many coins were in his charge.
However, the guards were uncooperative, and the best that Sagaris could get from each was a statement about the numbers of coins in the other two vaults.
- Dolius, who was guarding the gold, said there were 3000 silver and 5000 bronze coins.
- Termerus, who was in charge of the silver, said there were 3000 gold and 5000 bronze coins.
- Battus, who was protecting the bronze, said there were 4000 gold and 3000 silver coins.
If there were 12,000 coins altogether, how many of each type were there?