tonight my daughter brought home this problem and it's due by morning.
I personally think it unsolvable without college-level algebra, but obviously her teacher does not. I'd/We'd really appreciate any help anyone could give.
a) X is part of both the basketball and soccer circles, but not part of the table-tennis circle. So X represents the number of pupils who are taking both basketball and soccer, but not table-tennis.
b) In brief note that Y is a part of all three circles. So Y represents the number of pupils participating in all three sports.
For the record, this is grade level Mathematics. Some applications of Venn diagrams can get complicated, but these are just basic definitions.
-Dan
Whoops! Okay then, this is a bit higher level than I had thought.
And either I'm doing something wrong or the numbers in the problem aren't correct. I get a negative value for X. Here's the setup:
We know that the total number playing baseball is
$\displaystyle 36 + 18 = 54$
from the table and
$\displaystyle 22 + 9 + X + Y$
from the Venn diagram. So
$\displaystyle 22 + 9 + X + Y = 54$
We also know that the total number playing soccer is
$\displaystyle 49 + 14 + X + Y = 64 + 22$
and playing table-tennis is
$\displaystyle 9 + 14 + Y = 22 + 28$
From this last equation we get Y:
$\displaystyle 23 + Y = 50$
$\displaystyle -23 + 23 + Y = -23 + 50$
$\displaystyle Y = 27$
We may use either of the other two equations to get X:
$\displaystyle 22 + 9 + X + Y = 54$
So
$\displaystyle 22 + 9 + X + (27) = 54$
$\displaystyle 58 + X = 54$
$\displaystyle -58 + 58 + X = -58 + 54$
$\displaystyle X = -4$
(The other equation gives the same result. It's consistent anyway!)
If I made a mistake somewhere, please let me know.
-Dan