Out of 65 players,11 play basketball only,11 play both basketball and cricket.The number of players who play cricket is twice the number of players who play basketball.By using a venn diagram find the number of players who play cricket only and who don't play both the games
Did you fill in the given data ?
Draw two intersecting circles, label them B and C
In the intersection of B and C, enter 11
in the part of ' B only ' enter 11
so 22 play Basketball
"The number of players who play cricket is twice the number of players who play basketball" -----> so 44 play Cricket, and from your Venn you can see that the 'C only' part has to be 33
but 65 - 22 - 33 = 10
So 33 play only cricket, and 10 play neither sport.
Ah, the wonderful world of Venn diagrams, where circles come together to create chaos! Let's sort this out with a touch of humor.
First, we know that the number of players who play basketball only is 11. Let's call them the "Strict Ballers." 🏀
Next, we have 11 players who enjoy the best of both worlds, playing both basketball and cricket. These awesome folks shall be known as the "Double All-Rounders." 🏀🏏
According to the given information, the number of cricket players is twice the number of basketball players. So if we halve the number of basketball players (11), we get 5.5. But since nobody wants half a player (it's not like they can play with just one shoe), let's make it 5 and satisfy our mathematician friends by rounding down. These talented individuals shall be called the "Pure Cricket Lovers." 🏏
Now, let's figure out the remaining players. Since the number of cricket players is twice the number of basketball players, we can subtract the Double All-Rounders (11) and the Pure Cricket Lovers (5) from the total number of cricket players. This leaves us with 65 - 11 - 5 = 49 players, who we shall affectionately refer to as the "Mysterious Game Hoppers." They neither play basketball nor cricket exclusively! 🎭
To summarize:
- Basketball only (Strict Ballers): 11 players
- Basketball and cricket (Double All-Rounders): 11 players
- Cricket only (Pure Cricket Lovers): 5 players
- Neither basketball nor cricket (Mysterious Game Hoppers): 49 players
Remember, these quirky categories are just for fun, but the numbers are based on the given information.
To solve this problem using a Venn diagram, we can start by drawing two overlapping circles, one for basketball and one for cricket.
Let's represent the number of players who play basketball only as 'B', the number of players who play both basketball and cricket as 'C', and the number of players who play cricket only as 'A'.
According to the given information:
- The total number of players is 65.
- The number of players who play basketball only is 11.
- The number of players who play both basketball and cricket is 11.
- The number of players who play cricket is twice the number who play basketball.
We can now fill in the information on the Venn diagram:
Basketball (B)
/ \
/ \
/ \
Cricket (A) Both (C)
Since the number of players who play basketball is 11 and the number of players who play both basketball and cricket is also 11, we can write:
B = 11
C = 11
From the information given, we know that the number of players who play cricket is twice the number of players who play basketball. This means that:
A = 2B
Now we can substitute the value of B from the first equation into the second equation:
A = 2(11)
A = 22
The Venn diagram now looks like this:
Basketball (11)
/ \
/ \
/ \
Cricket (22) Both (11)
Now we can find the number of players who play cricket only and who don't play both games. These are the players only in the cricket circle but not in the overlap section:
Number of players who play cricket only = A - C
Number of players who don't play both = A - C
Substituting the values we have:
Number of players who play cricket only = 22 - 11 = 11
Number of players who don't play both = 11 - 11 = 0
So, there are 11 players who play cricket only and 0 players who don't play both games.
To find the number of players who play cricket only and who don't play both games, we can use a Venn diagram.
Step 1: Draw two overlapping circles to represent basketball and cricket.
Step 2: Label the left circle "Basketball" and the right circle "Cricket".
Step 3: Write down the given information. We know that there are 65 players in total, 11 of whom play only basketball, and 11 who play both basketball and cricket.
Step 4: Let's denote the number of players who play basketball only as "x" and the number of players who play cricket only as "y". We are also given that the number of players who play cricket is twice the number of players who play basketball. So, we can say y = 2x.
Step 5: Fill in the information we know. We have 11 players in the basketball-only section, and 11 players in the overlapping region for both basketball and cricket.
Step 6: Now, we can use this information to solve for x and y. We can set up the following equation based on the information we have: x + 11 + 11 + y = 65.
Step 7: Simplify the equation: x + y + 22 = 65.
Step 8: Rearrange the equation: x + y = 65 - 22.
Step 9: Simplify further: x + y = 43.
Step 10: Substitute the value of y from step 4 into the equation from step 9: x + 2x = 43.
Step 11: Simplify: 3x = 43.
Step 12: Solve for x: x = 43/3.
Step 13: Find the value of y using the equation from step 4: y = 2 * (43/3).
Step 13: Calculate x and y: x ≈ 14.33 (rounded to the nearest whole number, x = 14) and y ≈ 28.67 (rounded to the nearest whole number, y = 29).
Step 14: Now, we have the number of players who play basketball only (x = 14) and the number of players who play cricket only (y = 29).
Therefore, the number of players who play cricket only and don't play both games is 29.