The 90 members of a sport 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 volleyball. n people play all three games. 2n people each play only one game. How many play football altogether?

I don't know so help me

To determine how many people play football altogether, we need to use the principle of inclusion-exclusion and analyze the given information step by step.

Let's assign variables to the different sets:
T: Number of people playing Tennis
F: Number of people playing Football
V: Number of people playing Volleyball
n: Number of people playing all three games

From the given information, we know the following:
1. 10 people play Tennis and Football (T ∩ F = 10)
2. 19 people play Football and Volleyball (F ∩ V = 19)
3. 29 people play Tennis and Volleyball (T ∩ V = 29)
4. 2n people play only one game (T ∪ F ∪ V - 3n = 2n)

Using this information, we can set up equations:
10 + n + 19 + n + 29 + n + 2n = 90, since the total number of people in the club is 90
61 + 5n = 90
5n = 90 - 61
5n = 29
n = 29 / 5
n = 5.8

Since the number of people cannot be fractional, we conclude that n = 5.

Now we can calculate the number of people playing only one game:
T ∪ F ∪ V - 3n = 2n
90 - 3(5) = 2(5)
90 - 15 = 10
75 = 10

Substituting the values obtained, we can determine the number of people playing Football:
F = T ∪ F - (T ∩ F) - (F ∩ V) - n
F = (10 + 2(5)) - 10 - 19 - 5
F = 20 - 10 - 19 - 5
F = 20 - 10 - 19 - 5
F = 20 - 29
F = -9

However, the result F = -9 is not possible, as it represents a negative number of people playing football. Therefore, it seems there might be an error or inconsistency in the given information.

Double-check the information provided to ensure its accuracy.