Club football tennis

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?

Final Answer:

F =  220
T =  22

Step-by-step explanation:

$$\begin{gathered} x=F\cap T \\ F+T-x+z=302 \\ F=10\cdot T \\ (F-x)+(T-x)=222 \\ z+T-x=82 \\ F+T-x+z=302 \\ F-10T=0 \\ F+T-2x=222 \\ T-x+z=82 \\ Row2-Row1\to Row2 \\ -11T+x-z=-302 \\ Row3-Row1\to Row3 \\ -x-z=-80 \\ Row4-\frac{1}{-11}\cdot Row2\to Row4 \\ -0.9091x+0.9091z=54.5455 \\ Row4-\frac{-0.90909091}{-1}\cdot Row3\to Row4 \\ 1.8182z=127.2727 \\ z=\frac{127.27272727}{1.81818182}=70 \\ x=\frac{-80+z}{-1}=\frac{-80+70}{-1}=10 \\ T=\frac{-302-x+z}{-11}=\frac{-302-10+70}{-11}=22 \\ F=302-T+x-z=302-22+10-70=220 \\ F=220 \\ T=22 \\ x=10 \\ z=70 \end{gathered}$$

$T=22$

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