Question 1164746: In a group of 30 boys, 19 are on the football
team, 17 are on the soccer team, and 10 are on
both teams. Three of the boys play basketball,
football, and soccer. Five boys play soccer and
basketball, and nine play football and
basketball. All the boys are on at least one team.
How many boys play basketball only?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
If 3 play all three sports, and 10 play both football and soccer, the 7 (10 minus the 3 that do all three) play ONLY F and S. Likewise, 5 play both S and B, so 5 minus 3 = 2 play ONLY S and B. And then 9 minus 3 is 6 play only F and B. The 7 that play ONLY F and S, the 3 that play all three, and the 6 that play only F and B add up to 16 that play F and something else, so 19 minus 16 leaves 3 that play F ONLY. Likewise, 5 play S ONLY. Summary:
F only 3
S only 5
F and S only 7
F and B only 6
S and B only 2
All three 3
These add up to 26. Since all 30 boys did something...
You can figure the rest.
John
My calculator said it, I believe it, that settles it
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