Last year the number of students in a school was 750. This year the number of male students has decreased by 9%, whereas the number of female students has increased by 20%. The net change in students is an increase of 34. What is the number of female students this year? (a problem from Brilliant.org)

Question

phi · Answer

you could start by saying the number of girls + number of boys equals 750

g+b= 750

also, 20% increase in girls minus 9% decrease in boys equals 34 
so 0.20g - 0.09b =34

we now have 2 equations and 2 unknowns that can be solved.