Sets - Very urgent (O levels/GCSE)

• Sep 19th 2007, 06:12 AM
Anant Kapoor
Sets - Very urgent (O levels/GCSE)
At a sports centre, members are able to play badminton (B), squash (S) and table tennis (T).

The 140 members all play atleast 1 game but some play all 3.
42 members play table tennis only; and 16 play squash only.
25 members play both squash and table tennis.
The number of members who play badminton only is twice the number who play all 3 games.

a) denote the number of members who play all 3 games by x.
b)form an equation in x and solve it.

Thanks Anant
• Sep 19th 2007, 07:41 AM
TKHunny
The hardest part of this problem is paying attention -- really!

Draw three intersecting circles. make sure each intersects its two neighbors and they all intersect each other in the middle. This should give you a region divided up into seven (7) sub regions. There should be one piece in all three circles. There should be three pieces in two circles each. There should be three pieces that are part of only one circle. Each circle should be in four regions,

Label the three circles as you wish, probably with a B, S, and T.

Now, take each phrase and translate it with a number or expression in one or more of the seven regions.

"The 140 members "

The sum of all seven regions is 140

"18 play both badminton and squash."

The two regions shared between B and S should add to 18

"42 members play table tennis only"

The region from T that intersects no other circle has 42.

"and 16 play squash only."

The region from S that intersects no other circle has 16.

"25 members play both squash and table tennis."

The two regions shared by S and T should sum to 25

"The number of members who play badminton only is twice the number who play all 3 games."

The region from B that intersects no other circle has 2 times the value from the very center.

After all that, you just have to wade through the arithmetic. You may need to invent a naming convention for ech of the seven regions. That may help you keep track.

Note: What I have described is a general solution to the entire tournament. If you REALLY want just 'x', there may be a somewhat more straight-forward pathway.