Halmar the Great has boasted to his hordes of followers that many a notorious villain has fallen to his awesome sword: His total of 580 victims consists of evil sorcerers, trolls, and orcs. These he has slain with a total of 660 mighty thrusts of his sword; evil sorcerers and trolls each requiring two thrusts (to the chest) and orcs each requiring one thrust (to the neck). When asked about the number of trolls he has slain, he replies, "I, the mighty Halmar, despise trolls three times as much as I despise evil sorcerers. Accordingly, three times as many trolls as evil sorcerers have fallen to my sword!" How many of each type of villain has he slain?
Halmar the Great has boasted to his hordes of followers that many a notorious villain has fallen to his awesome sword: His total of 580 victims consists of evil sorcerers, trolls, and orcs. These he has slain with a total of 660 mighty thrusts of his sword; evil sorcerers and trolls each requiring two thrusts (to the chest) and orcs each requiring one thrust (to the neck). When asked about the number of trolls he has slain, he replies, "I, the mighty Halmar, despise trolls three times as much as I despise evil sorcerers. Accordingly, three times as many trolls as evil sorcerers have fallen to my sword!" How many of each type of villain has he slain?
Let the number of evil sorcerers be x, the number of trolls is y, and the number of orcs is z.
Then x + y + z = 580
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