Halmar the Great has boasted to his hordes of followers that many a notorious villain has fallen to his awesome sword: His total of 700 victims consists of evil sorcerers, trolls, and orcs. These he has slain with a total of 900 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 nine times as much as I despise evil sorcerers. Accordingly, nine times as many trolls as evil sorcerers have fallen to my sword!" How many of each type of villain has he slain?

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Halmar the Great has boasted to his hordes of followers that many a notorious villain has fallen to his awesome sword: His total of 700 victims consists of evil sorcerers, trolls, and orcs. These he has slain with a total of 900 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 nine times as much as I despise evil sorcerers. Accordingly, nine times as many trolls as evil sorcerers have fallen to my sword!" How many of each type of villain has he slain?
 
sorcerers _____
trolls _____
orcs _____
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