In a class of 50 students, 25 play chess, 17 play squash 13 do not play any game at all. Find the number of students who play both chess and squash
Let x be the number plalying both
25+17+13-x = 50
x = 5
You can illustrate this with a Venn Diagram
To find the number of students who play both chess and squash, we can use the principle of inclusion-exclusion:
Step 1: Start with the total number of students (50).
Step 2: Subtract the number of students who do not play any game (13).
Step 3: Subtract the number of students who play only chess (25 - x).
Step 4: Subtract the number of students who play only squash (17 - x).
Step 5: Equate the above number to the total number of students playing both games.
Step 6: Solve for x.
Let's write the equation:
50 - 13 = (25 - x) + (17 - x) + x
Simplifying this equation:
37 = 42 - x
Subtracting 42 from both sides:
-5 = -x
Multiplying both sides by -1:
5 = x
Therefore, the number of students who play both chess and squash is 5.
To find the number of students who play both chess and squash, we need to use the principle of inclusion-exclusion.
We know that there are 50 students in the class. Let's assign variables to represent the sets:
- let C represent the set of students who play chess
- let S represent the set of students who play squash
According to the given information:
- |C| = 25 (number of students who play chess)
- |S| = 17 (number of students who play squash)
- |C ∪ S| = 50 (total number of students in the class)
- |C ∩ S| (number of students who play both chess and squash) is what we need to find.
The principle of inclusion-exclusion states that:
|C ∪ S| = |C| + |S| - |C ∩ S|
We can substitute the known values into the equation:
50 = 25 + 17 - |C ∩ S|
Rearrange the equation to find the number of students who play both chess and squash:
|C ∩ S| = 25 + 17 - 50
Simplify the equation:
|C ∩ S| = 42 - 50
|C ∩ S| = -8
Since the number of students cannot be negative, there seems to be an error or inconsistency in the given information or calculations. Please double-check the given data or the calculations.