The 90 members of a sports club play at least one of the games,tennis,football and volleyball. 10 play tennis and football,19 play football and volley ball,and 29 play tennis and volley ball. n people play all three games. 2n people each play only one game. How many play football altogether?

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To find n we have:

2n+2n+2n+10−n+19−n+29−n+n=90

4n=32

n=8

Now to find the total number of people that play football, we have:

F=2n+10−n+19−n+n=29+n=37

Venn diagram

To find out how many people play football altogether, we need to use the principle of inclusion-exclusion.

Let's break down the information given:
- 10 people play tennis and football
- 19 people play football and volleyball
- 29 people play tennis and volleyball
- n people play all three games
- 2n people play only one game

To find the total number of people who play football, we need to add up the number of people who play only football and the number of people who play football along with other games.

Let's calculate the number of people who play only football:
The total number of people who play only one game is given as 2n. Since n people play all three games, we can conclude that n people play football only. Therefore, the number of people who play only football is n.

Now, let's calculate the number of people who play football with other games:
The total number of people who play tennis and football is 10, including the people who play all three games. Therefore, the number of people who play tennis and football without playing volleyball is 10 - n.
Similarly, the number of people who play football and volleyball without playing tennis is 19 - n.
And the number of people who play tennis and volleyball without playing football is 29 - n.

To find out how many people play football along with other games, we can add up the number of people who play tennis and football, football and volleyball, and subtract the number of people who play all three games:
(10 - n) + (19 - n) - (29 - n)

Simplifying the expression further:
10 + 19 + 29 - 3n

Now, to find the total number of people playing football, we need to add the number of people who play only football and the number of people who play football along with other games:
n + (10 + 19 + 29 - 3n)

Simplifying further:
n + 58 - 2n

Combining like terms:
58 - n

Hence, the total number of people who play football altogether is 58 - n.

Please how did you get 32