Algebra

[Guest]

In a school 315 girls play at least one sport. 100 play a fall sport, 150 play a winter sport, and 200 play a spring sport. If 75 girls play exactly 2 sports, how many play three?

[shyamjayakannan]

let x, y and z be the numbers of girls playing 1, 2 and 3 games, respectively. So, [tex]x+y+z=315[/tex], [tex]x+2y+3z=100+150+200[/tex] and [tex]y=75[/tex].
So, [tex]x+z=240[/tex] and [tex]x+3z=300[/tex] and from this, we get [tex]\boxed{z=30}[/tex].