Question

When the members of a family discussed where their annual reunion should take​ place, they found that out of all the family​ members, 1010 would not go to a​ park, 88 would not go to a​ beach, 1212 would not go to the family​ cottage, 55 would go to neither a park nor a​ beach, 44 would go to neither a beach nor the family​ cottage, 77 would go to neither a park nor the family​ cottage, 33 would not go to a park or a beach or to the family​ cottage, and 11 would go to all three places. What is the total number of family​ members?

Answer 1

2178

Explanation:

We are given that

Number of members would not go to a park=1010

Number of members would not go to a beach=88

Number of members would not go to the family cottage=1212

Number of members would go to a neither a park nor beach=55

Number of members would go to neither a beach nor the family cottage=44

Number of members would go to neither a park nor the family cottage=77

Number of members would not go to a park or a beach or to the family cottage=33

Number of members would go to all three places=11

s=Number of non park goers only

t=Number of non park goers and non beach goers but not non family cottage goers

u=Number of non beach goers only

v=Number of non park goers and non family cottage goers but not non beach goers

w=Number of non park goers, non beach goers and non family cottage goers

x=Number of non beach goers, non family cottage goers but not non park goers

y=Number of non family cottage goers only

z=Number of not non park goers, not non beach goers and not non family cottage goers

According to question

`s+t+v+w=1010`

`t+u+w+x=88`

`v+w+x+y=1212`

`t+w=55`

`w+x=44`

`v+w=77`

`w=33`

`z=11`

`v=77-w=77-33=44`

`t=55-w=55-33=22`

`x=44-w=44-33=11`

`22+u+33+11=88`

`u=88-66=22`

`44+33+11+y=1212`

`y=1212-88=1124`

`s+22+44+33=1010`

`s=1010-99=911`

Total number of family members=s+t+u+v+w+x+y+z=911+1124+22+11+22+44+11+33=2178

Hence, total number of family members=2178