An algebra problem by A Former Brilliant Member

Here is something fun and interesting to think about.

If there are $45\%$ of the people who are girls after $6$ girls are replaced by $6$ boys, then the total number of boys and girls do not change. In fraction form, $45\% = \dfrac{9}{20}$ . Multiply the top and bottom by $6$ , so we have $54$ girls out of $120$ people.

Since $6$ girls are replaced by $6$ boys, add $54$ by $6$ to get $m = 60$ ! :D

total number of students = 2m

our working equation is

$\frac{m-6}{2m}$ $=0.45$

after simplifying, we get

$m=60$