11o members of a sports club play at least one of the games, football basketball and volleyball. If 20 play football and basketball only,15 play football and volleyball only, 26 play basketball and volleyball only, x play all the three game,2x each play only one game, how many play basketball altogether?

Answer 1

if you draw the Venn diagram, you can easily see that
20+26+15+x+2x+2x+2x = 110
find x, and then you want 20+26+2x+x

Answer 2

I made my Venn diagram, filled in the data
x in the middle, 20-x, 15-x, and 26-x for the corresponding 2-item sports, and 2x in each of the circles, for students involved in only one sport.
My equation is
2x + x + (20 - x) + (15 - x) + 2x + (26 - x) + 2x = 110
4x = 49
x = 49/4 ,which is not a whole number since x represents number of students

I think your data is flawed.

The solution for oobleck's equation is
x = 7
filling in the Venn diagram with that solution, gives a total of 89 students involved in the 3 sports, not 110 as needed.

Answer 3

better recheck your figures, Reiny. There's no "-x" needed, since it says

20 play football and basketball only

That is, the x in the center does not need to be subtracted from each intersection.

Answer 4

I stand corrected, skimmed and stumbled over that "only"
Assumed the usual wording for this type of question