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:

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

$T=22$

Try another example