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?

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Mathematics

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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 :

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lublana lublana · Answer 1 · 2025-03-23T07:00:25-04:00

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

[tex]s+t+v+w=1010[/tex]

[tex]t+u+w+x=88[/tex]

[tex]v+w+x+y=1212[/tex]

[tex]t+w=55[/tex]

[tex]w+x=44[/tex]

[tex]v+w=77[/tex]

[tex]w=33[/tex]

[tex]z=11[/tex]

[tex]v=77-w=77-33=44[/tex]

[tex]t=55-w=55-33=22[/tex]

[tex]x=44-w=44-33=11[/tex]

[tex]22+u+33+11=88[/tex]

[tex]u=88-66=22[/tex]

[tex]44+33+11+y=1212[/tex]

[tex]y=1212-88=1124[/tex]

[tex]s+22+44+33=1010[/tex]

[tex]s=1010-99=911[/tex]

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