2021 Fall AMC 10B Problems/Problem 9
Contents
Problem
The knights in a certain kingdom come in two colors. of them are red, and the rest are blue. Furthermore,
of the knights are magical, and the fraction of red knights who are magical is
times the fraction of blue knights who are magical. What fraction of red knights are magical?
Solution 1
Let be the number of knights: then the number of red knights is
and the number of blue knights is
.
Let be the fraction of blue knights that are magical - then
is the fraction of red knights that are magical. Thus we can write the equation
We want to find the fraction of red knights that are magical, which is
~KingRavi
Solution 2
We denote by the fraction of red knights who are magical.
Hence,
By solving this equation, we get .
Therefore, the answer is .
~Steven Chen (www.professorchenedu.com)
Video Solution 1
~Education, the Study of Everything
Video Solution by Interstigation
https://youtu.be/p9_RH4s-kBA?t=1274
See Also
2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.