The Downfall of the Magicians

Algebra Level 2

At the Magicians Rave Palace, there are 500 magicians. A fight occurred between the 500 magicians and the 500 demons. The magicians won, and all of the demons died, but we don't know how many magicians died, and how many lived. You were able to gather some clues that you can use to crack the case.
$x$ number of magicians died from a demon's weapon.
$2x$ number of magicians were killed by traps.
$x - 94$ number of magicians died from fever.
( $20\%$ of $x$ ) number of magicians were killed by magician spells reflecting off their wands and hitting them.
$x$ = (Unlucky Number) times $10$ minus $10$
How many magicians survived?

1 solution

Vishruth K
Mar 24, 2021

For most people, the unlucky number is 13.
13 times 10 = 130.
130 minus 10 = 120, so $x$ = 120.
120 magicians died from a demon's weapon.
120 times 2 = 240.
240 magicians were killed by traps.
120 minus 94 = 26.
26 magicians were killed by fever.
20% of 120 = 120 divided by 5 = 24.
24 magicians died from magician spells reflecting off their wands and hitting them.
120 + 240 + 26 + 24 = 410, so 410 magicians died.
500 minus 410 = 90, so 90 magicians survived.
Thus, our answer is 90 .