110 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 basketball only, 26 play basketball and volleyball only,x play all the three games, 2x each play only one game, how many play basketball altogether
I need the venn diagram please
You have listed playing football and basketball playing twice, with different numbers.
I will conclude that the second football and basketball should be football and volleyball.
Made a Venn diagram filled in the data as given, and got this equation.
2x + 2x + 2x + x + 20+15+26 = 110
7x = 49
x = 7
so the basketball circle
= 2x+x+20+26 =
3x + 46 = 67
I need the venn diagram of the answer please
67
How did you arrive at 52?
To find out how many people play basketball altogether, we need to add up the number of people who play basketball only and the number of people who play basketball along with other games.
Let's break down the given information:
- 20 people play football and basketball only
- 15 people play football and basketball only
- 26 people play basketball and volleyball only
- x people play all three games
- 2x people each play only one game (assuming x is the same for all three games)
To proceed, we will use a method called the Principle of Inclusion-Exclusion.
Step 1: Calculate the total number of people who play at least one game.
We know that the total number of members in the sports club is 110. From this, we can subtract the number of people who don't play any game.
Let's calculate the number of people who don't play any game:
Total number of members - Total number of people who play at least one game
= 110 - (20 + 15 + 26 + 2x)
= 110 - (61 + 2x)
So, the number of people who don't play any game is 110 - (61 + 2x).
Step 2: Calculate the number of people who play basketball only.
We know that 2x people each play only one game. Since we are interested in finding the number of people who play basketball only, we need to consider the number of people who play basketball and not any other game. That means we need to subtract the number of people who play basketball along with other games:
Number of people who play basketball only = Number of people who play basketball and not any other game
= (Total number of people who play basketball) - (Number of people who play basketball and football only) - (Number of people who play basketball and volleyball only) + (Number of people who play all three games)
Note: When we subtract the people playing basketball and other games, we need to add back the people playing all three games since they were subtracted twice.
Let's calculate the number of people who play basketball only:
Number of people who play basketball only = (Total number of people who play basketball) - (15) - (26) + (x)
Step 3: Calculate the number of people who play basketball altogether.
To find out the total number of people who play basketball altogether, we need to add the number of people who play basketball only to the number of people who play basketball along with other games:
Total number of people who play basketball altogether = Number of people who play basketball only + (Number of people who play basketball and football only) + (Number of people who play basketball and volleyball only) + (Number of people who play all three games)
Total number of people who play basketball altogether = (Number of people who play basketball only) + 20 + 26 + x
Now, let's substitute the values we have and simplify the equation:
Total number of people who play basketball altogether = [(Total number of people who play basketball) - 15 - 26 + x] + 20 + 26 + x
= [(110 - (61 + 2x)) - 15 - 26 + x] + 20 + 26 + x
= (110 - 61 - 15 - 26 + x - 2x) + 20 + 26 + x
= (8 + x) + 20 + 26 + x
= 54 + 2x
Therefore, the total number of people who play basketball altogether is 54 + 2x.