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Question 1161882: 33 of the students in a class play either football or table tennis. If 22 students play football and 18 play table tennis, how many students play football only
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
33 of the students in a class play either football or table tennis.Let x = the number who play football but don't play table tennis.
Let y = the number who play football and also play table tennis.
Let z = the number who play table tennis but do not play football.
x + y + z = 33 If 22 students play footballx + y = 22 and 18 play table tennis,y + z = 18
Subtract the third equation from the first:
x + y + z = 33
y + z = 18
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x = 15
how many students play football only.
Answer = 15.
Edwin
Answer by ikleyn(52756)  (Show Source):
You can put this solution on YOUR website! .
The solution by Edwin is good and correct;
but I want to show you much more educational version.
In elementary set theory, there is the identity for numbers of elements in finite sets.
If A and B are finite subsets in an universal set U, then
n(A U B) = n(A) + n(B) - n(A intersection B). (1)
It says that the number of elements in the union of two subsets is the sum
of the numbers of elements in subsets minus number of elements in the intersection.
This formula and this statement are almost self-evident, but you need to know WHY.
When we want to determine the number of elements in the union of the subsets, taking the sum is a good initial estimation.
But doing this way, we count the elements in the intersection twice.
Therefore, we correct the formula and subtract elements of the intersection.
So, substituting the given values into the formula (1), you get
33 = 22 + 18 - n(football AND tennis).
It gives you the number of those students who play both sports
n(fotball AND tennis) = 32 + 18 - 33 = 40 - 33 = 7.
Now, to get the number of those who play football only, you subtract 7 (intersection) from 22 (football).
In this way, you get the
ANSWER. 22-7 = 15 students play football only.
Solved.
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In your school/college/university years you will meet such/similar problems hundreds of times.
So, learn this method.
See the lesson
- Counting elements in sub-sets of a given finite set
in this site.
Happy learning and have fun (!)
Come again to this forum soon to learn something new and useful (!)
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