Answer to Question #134141 in Algebra for camm

Question

Aragorn The Great has boasted to his hordes of followers that many a notorious villian has fallen
to his awesome sword: His total of 560 victims consists of evil sorcerers, trolls, and orcs. These he
has slain with a total of 620 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 Aragorn, despise trolls five times as much as I despise
evil sorcerers. Accordingly, five times as many trolls as evil sorcerers have fallen to my sword!” How
many of each type of villian has he slain

Answer 1

Create equations with infomation:

x - sorcerers

y - trolls

z - orcs

1) x + y + z = 560

2) x +5x + z = 560

3) 2x + 2y + z = 620

from 2) equation:

4) z = 560 - 6x

Also we know that y = 5x, so from 3) and 4) equations:

2x + 10x + 560 - 6x = 620

6x = 60 , so x = 10.

from y = 5x we have y = 50

And using 1) equation we have:

z = 560 - 10 - 50, z = 500

Answer: evil sorcerers - 10, trolls - 50, orcs - 500