all the pupils on the class of 35 play atlist one the games volleyball, netball , hockey 10 play volley ball only , 5 netball only and 3 play hockey only if 2 play all three games and equal numbers play 2 games ::: how many altogether play volleyball
If x = 5, then the total number of students who play volleyball is:
10 (play volleyball only) + 2 (play all three games) + 2x (play two games) = 10 + 2 + 2(5) = 22
Therefore, 22 students altogether play volleyball.
Draw your Venn diagram. You can see that if x play two games, then
10+5+3+3x+2 = 35
Find x, and then 10+3+2x play volleyball.
5
To find out how many pupils play volleyball, we need to determine the number of pupils who play volleyball only and those who play volleyball along with other games.
Given that 10 pupils play volleyball only and 2 pupils play all three games, we can subtract these two numbers from the total number of pupils playing games to find the number of pupils who play volleyball along with other games.
Total number of pupils playing games = 35
Number of pupils playing volleyball only = 10
Number of pupils playing all three games = 2
Number of pupils playing volleyball along with other games = Total number of pupils playing games - Number of pupils playing volleyball only - Number of pupils playing all three games
Number of pupils playing volleyball along with other games = 35 - 10 - 2
Number of pupils playing volleyball along with other games = 23
However, we are also told that an equal number of pupils play two games. Since there are three games in total, we need to divide the remaining pupils (who play volleyball along with other games) by 2 to get the number of pupils who play volleyball and another game.
Number of pupils who play volleyball and another game = (Number of pupils playing volleyball along with other games) / 2
Number of pupils who play volleyball and another game = 23 / 2
Number of pupils who play volleyball and another game = 11.5
Since the number of pupils is a whole number, we can conclude that there are 11 pupils who play volleyball and another game.
To find the total number of pupils who play volleyball, we need to add the number of pupils who play volleyball only to the number of pupils who play volleyball and another game.
Total number of pupils playing volleyball = Number of pupils playing volleyball only + Number of pupils who play volleyball and another game
Total number of pupils playing volleyball = 10 + 11
Total number of pupils playing volleyball = 21
Therefore, 21 pupils play volleyball.