All the people in a class of 35 play at least one of the games volleball,netball and hockey.10 play volleball only,5 play netball only and 3 play hockey only.if 2 play many of all 3 gamez and the equal number play 2 games.how many altogether play volleball
Adding up all the players named, we have 10+5+3+2 = 20 players. That leaves 15 people divided equally among the two-game areas. So, 5 play volleyball and netball and 5 play volleyball and hockey.
So, 10+5+5+2=22 play volleyball.
Just draw a Venn diagram and fill in the named regions.
To find out how many people altogether play volleyball, we need to add up the number of people who play volleyball only, the number of people who play multiple games, and the number of people who play all three games.
Let's break down the information given:
- 10 people play volleyball only.
- 5 people play netball only.
- 3 people play hockey only.
- 2 people play all three games.
- An equal number of people play two games.
To find the number of people who play multiple games, we need to consider that the same number of people play two games. Since we have 10 people playing volleyball only, 5 people playing netball only, and 3 people playing hockey only, a total of 18 people play only one game (10 + 5 + 3 = 18). So, the remaining players must be the ones playing multiple games.
Since 2 people play all three games, there are 18 people left who play some combination of two games. Since the number of players is equal for each game, we can divide these 18 people into 6 groups of two games each. This means that 6 people play volleyball and netball, 6 people play netball and hockey, and 6 people play volleyball and hockey.
To find the total number of people who play volleyball, we add up the number of people who play volleyball only (10) and the number of people who play volleyball along with another game (6 for volleyball and netball, and 6 for volleyball and hockey). The total number of people who play volleyball is 10 + 6 + 6 = 22.
Therefore, 22 people altogether play volleyball.