Eighty-two 80493

The sports club has 302 members. Ten times more members play soccer than tennis. Just one of the sports (F and T) is played by 222 members. Eighty-two members do not play football. How many members of the club play football? How many members play tennis?

Correct answer:

F =  220
T =  22

Step-by-step explanation:

x=F∩T  F+T−x+z=302 F=10⋅ T (F−x)+(T−x)=222 z+T−x=82  F+T−x+z=302 F−10T=0 F+T−2x=222 T−x+z=82  Row2−Row1→Row2 F+T−x+z=302 −11T+x−z=−302 F+T−2x=222 T−x+z=82  Row3−Row1→Row3 F+T−x+z=302 −11T+x−z=−302 −x−z=−80 T−x+z=82  Row4−−111​⋅ Row2→Row4 F+T−x+z=302 −11T+x−z=−302 −x−z=−80 −0.9091x+0.9091z=54.5455  Row4−−1−0.90909091​⋅ Row3→Row4 F+T−x+z=302 −11T+x−z=−302 −x−z=−80 1.8182z=127.2727  z=1.81818182127.27272727​=70 x=−1−80+z​=−1−80+70​=10 T=−11−302−x+z​=−11−302−10+70​=22 F=302−T+x−z=302−22+10−70=220  F=220 T=22 x=10 z=70
T=22

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