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

Answer:

2178

Step-by-step 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