The 79 members of a spot club play at least one of the following games Tennis, Football and Volleyball. 19 play Football & Volleyball and 29 play Tennis & Volleyball, n play all the three games. 2n people , each play only one game. How many play Volleyball altogether.?
Plzzzz help me
If x people play Football and Tennis, then add up the areas of the Venn diagram in the usual way, and you have
2n+19+29-n+x-n=79
x=31
See if that gets you started.
thanks sir but i already did that and i got 31 my problem is how to finalise it
To find out how many people play volleyball altogether, we need to add up the number of people who play volleyball in each category.
Let's go step-by-step to solve this problem:
Step 1: Find the number of people who play both football and volleyball.
Given: 19 people play Football & Volleyball.
Step 2: Find the number of people who play both tennis and volleyball.
Given: 29 people play Tennis & Volleyball.
Step 3: Find the number of people who play all three games.
Given: n people play all three games.
Step 4: Find the number of people who play only one game.
Given: 2n people play only one game.
Now, let's use these numbers to calculate the number of people who play volleyball:
Step 5: Find the number of people who play only football and volleyball.
To find this number, we need to subtract the number of people playing all three games from the number of people playing football and volleyball.
19 - n = 19n
Step 6: Find the number of people who play only tennis and volleyball.
To find this number, we need to subtract the number of people playing all three games from the number of people playing tennis and volleyball.
29 - n = 29n
Step 7: Find the number of people who play only volleyball.
To find this number, we need to subtract the number of people playing all three games, the number of people playing only football and volleyball, and the number of people playing only tennis and volleyball from the total number of members in the sports club.
79 - (19 + 29 + n + 19n + 29n) = 79 - (19 + 29 + n + 19n + 29n) = 79 - (48 + 49n) = 31 - 49n
Final Step: Find the total number of people who play volleyball.
To find this number, we add the number of people playing all three games, the number of people playing only football and volleyball, the number of people playing only tennis and volleyball, and the number of people playing only volleyball.
n + 19n + 29n + (31 - 49n) = n + 19n + 29n + 31 - 49n = 79
Now we have the equation:
n + 19n + 29n + 31 - 49n = 79
We can simplify this equation to solve for n:
-48n + 31 = 79
-48n = 48
n = 1
Now, we can substitute the value of n back into the equation to find the total number of people who play volleyball:
31 - 49(1) = 31 - 49 = -18
Since the number of people cannot be negative, there seems to be an error in the question or our calculations. Please double-check the information given to resolve the issue.
To find out how many people play Volleyball altogether, we need to add up the number of people playing Volleyball exclusively and those playing Volleyball in combination with other games.
Let's break down the information given:
1. There are 79 members in the sports club.
2. 19 people play both Football and Volleyball.
3. 29 people play both Tennis and Volleyball.
4. n people play all three games.
5. 2n people play only one game.
First, let's find out how many people play only one game. Since 2n people each play only one game, we can calculate that there are a total of 2n members.
Next, we can determine the number of people who play Volleyball exclusively. Since we know that 19 people play both Football and Volleyball, we subtract this from the total number of people playing only one game: 2n - 19.
Now we need to consider those who play Volleyball in combination with Tennis. We know that 29 people play both Tennis and Volleyball. However, we want to exclude those who play all three games, as they have already been counted in the previous step. So, to avoid double-counting, we subtract the number of people who play all three games, which is n: 29 - n.
Finally, to find the total number of people who play Volleyball altogether, we add these two groups of people: (2n - 19) + (29 - n).
Therefore, the total number of people who play Volleyball altogether is (2n - 19) + (29 - n).