Try this beautiful problem from the Pre-RMO, 2017 based on ratio.
In a sports team, the total number of boys and girls are in the ratio 4:3. On one day it was found that 8 boys and 14 girls were absent from the team and that the number of boys was the square of the number of girls, find the total number of members in the sports team.
Ratio
Integers
Algebra
But try the problem first...
Answer: is 42.
PRMO, 2017, Question 12
Elementary Algebra by Hall and Knight
First hint
here ratio = 4:3
\(\Rightarrow boys =4x, girls=3x\)
given \((4x-8)=(3x-14)^{2}\)
Second Hint
\(\Rightarrow 4x-8=9x^{2}-84x+196\)
\(\Rightarrow 9x^{2}+196-84x=4x-8\)
\(\Rightarrow 9x^{2}-88x+204=0\)
Final Step
\(x=\frac{88\pm\sqrt{88^{2}-4(9)(204)}}{18}\)
\(\Rightarrow x=6 or \frac{34}{9}\)
\(\Rightarrow 7x=42\) or non-integer
\(\Rightarrow 42 members.\)
Math Olympiad Program... taught by Olympians and researchers
From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here:
