Answer:
Step-by-step explanation:
To find the number of people who play basketball altogether, we need to analyze the given information step by step:
1. We know that there are 110 members in the sports club.
2. 20 members play both football and basketball only.
3. 15 members play both football and volleyball only.
4. 26 members play both basketball and volleyball only.
5. x members play all three games.
6. 2x members play only one game each.
To find the number of people who play basketball altogether, we can start by considering the members who play basketball in different scenarios:
Scenario 1: Members who play only basketball
Since 20 members play only football and basketball, we subtract 20 from the total number of basketball players.
Scenario 2: Members who play both basketball and one other game
Since 26 members play only basketball and volleyball, we subtract 26 from the total number of basketball players.
Scenario 3: Members who play all three games and basketball
Since x members play all three games, we include x in the total number of basketball players.
Scenario 4: Members who play only one game each and basketball
Since 2x members play only one game each, we include 2x in the total number of basketball players.
To calculate the total number of basketball players, we add the number of basketball players from each scenario:
Total number of basketball players = (Members who play only basketball) + (Members who play both basketball and one other game) + (Members who play all three games and basketball) + (Members who play only one game each and basketball)
Now, let's calculate the total number of basketball players step by step:
1. Members who play only basketball = 20
2. Members who play both basketball and volleyball = 0 (since we subtracted 26)
3. Members who play all three games and basketball = x
4. Members who play only one game each and basketball = 2x
Total number of basketball players = 20 + 0 + x + 2x
Simplifying the equation:
Total number of basketball players = 3x + 20
Therefore, the total number of people who play basketball altogether is 3x + 20.
