Chapter 4.3, Problem 11E

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7th Edition

Stefan Waner + 1 other

ISBN: 9781337274203

Textbook Problem

**Pest Control** Halmar the Great has boasted to his hordes of followers that many a notorious villain has fallen to his awesome sword: His total of 560 victims consists of evil sorcerers, trolls, and ores. 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 ores 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 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 villain has he slain?

To determine

**To calculate:** The number of each type of villain Halmar has slain. The victims include evil sorcerers, trolls and orcs. According to Halmar, the total number of victims were 560 for which he has slain 620 thrusts of his sword, the evil sorcerers and trolls require two thrusts each and orcs require only one thrust each. He despised trolls five times as much as evil sorcerers accordingly five times as many trolls as evil sorcerers have fallen to his sword.

Explanation

**Given Information:**

The victims include evil sorcerers, trolls and orcs. According to Halmar, the total number of victims were 560 for which he has slain 620 thrusts of his sword.

Also, the evil sorcerers and trolls require two thrusts each and orcs require only one thrust each. He despised trolls five times as much as evil sorcerers accordingly five times as many trolls as evil sorcerers have fallen to his sword.

**Formula Used:**

Elimination method:

In this method, we first combine the equations in a way such that one of the variables gets eliminated. Then we substitute this obtained value in either of the equation to get the value of the other variable.

**Calculation:**

Let the number of evil sorcerers, trolls, and orcs killed be

The given data shows the total number of victims is 560,

Thus, we can say that:

The total number of times he slew is 620 and sorcerers and trolls require two thrusts each.

Thus,

And he despised trolls five times as much as evil sorcerers accordingly five times as many trolls as evil sorcerers have fallen to his sword.

Thus,

Apply the elimination method to find the solution of the given system of the equations:

Begin by subtracting the first equation from the second equation to eliminate *z*

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