SOLUTION: In a group of 50 students at a summer school , 15 play tennis , 20 play cricket, 20 swim and 7 students do nothing. 3 students play tennis and cricket , 6 students play cricket and

Question 1090403: In a group of 50 students at a summer school , 15 play tennis , 20 play cricket, 20 swim and 7 students do nothing. 3 students play tennis and cricket , 6 students play cricket and swim , while 5 students play tennis and swim . How many do all three sports ?
Found 2 solutions by jorel1380, ankor@dixie-net.com:
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
Let those that do Tennis only be t, Cricket c and Swim s.
Let those that do all 3 sports be x.
so, Tennis and Cricket but not Swim => 3 - x
and Tennis and Swim but not Cricket => 5 - x
and Cricket and Swim but not Tennis => 6 - x
Tennis => t + 3 - x + x + 5 - x = 15
i.e. t = x + 7...(1)
Cricket => c + 3 - x + x + 6 - x = 20
i.e. c = x + 11...(2)
Swim => s + 5 - x + x + 6 - x = 20
i.e. s = x + 9...(3)
Now, considering all components we have:
t + c + s + 3 - x + x + 5 - x + 6 - x + 7 = 50
=> t + c + s - 2x + 21 = 50
i.e. t + c + s - 2x = 29
Using (1), (2) and (3) we have:
x + 7 + x + 11 + x + 9 - 2x = 29
i.e. x + 27 = 29
Hence, x = 2...i.e. 2 people play all three sports.
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Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
In a group of 50 students at a summer school, 15 play tennis, 20 play cricket, 20 swim and 7 students do nothing.
3 students play tennis and cricket, 6 students play cricket and swim, while 5 students play tennis and swim.
How many do all three sports?
:
subtract the ones that do nothing; 50-7 = 43 students play sport
:
15 - 5 - 3 = 8 students play only tennis
20 - 3 - 6 = 11 students play only cricket
20 - 6 - 5 = 9 students swim only
:
43 - 8 - 11 - 9 = 15 students play more than one sport
;
3 + 6 + 5 = 13 students play two sports
therefore
15 - 13 = 2 students play all 3 sports

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