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Math Help - VENN DIAGRAM Q thank you

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    VENN DIAGRAM Q thank you

    There are 40 members in a sports club. 2 play all three sports. 23 play squash. 24 play tennis. 18 play golf. 14 play squash and tennis. 8 play tennis and golf. 1 member makes the refreshments and does not play any sport. How many play squash and golf?
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    Senior Member vincisonfire's Avatar
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    Venn Diagram is not necessary but it is way much easier to figure the problem using it. This one consist of three circle.
    -You know that 14 play both tennis and squash. Because 2 play all sports, 12 play ONLY tennis and squash.
    -You know that 8 play both golf and tennis. Because 2 play all sports, 6 play ONLY golf and tennis.
    -You know that 24 play tennis and that 12+2+6 play tennis and something else so 4 play only tennis.
    Now you get this system of equations:
    Let x be the number of people that play only golf, y the number of people that play squash and golf but not all three sports and z the number of people that play only squash.
    18 = 6 + 2 + x + y
    23 = 12 + 2 + y + z
    39 = 24 + x + y + z
    You have three equations and three unknown. You can solve for y.
    Ans : y=4
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