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Answer:
20
Explanation:
Let:
• NP = The non-park goers.
,• NB = The non-beach goers.
,• NC = The non-cottage goers.
The Venn diagram below is used to represent the given information:
Given:
• There are 10 non-park goers: a+b+c+g=10
,• There are 9 non-beach goers: b+d+e+g=9
,• There are 11 non-cottages goers: c+e+f+g=11
,• There are 3 non-park and non-beach goers: b+g=3
,• There are 4 non-beach and non-cottage goers: e+g = 4
,• There are 6 non-park and non-cottage goers: c+g=6
,• There is 1 non-park, non-beach, and non-cottage goer: g=1
,• There are 2 who are neither a non-park, non-beach, or non-cottage goer: h=2
So, the total number of family members will be:
[tex]Total=a+b+c+d+e+f+g+h[/tex]Since g=1:
[tex]\begin{gathered} b+g=3\implies b+1=3\implies b=2 \\ c+g=6\operatorname{\implies}c+1=6\operatorname{\implies}c=5 \\ e+g=4\operatorname{\implies}e+1=4\operatorname{\implies}e=3 \end{gathered}[/tex]Next:
[tex]\begin{gathered} c+e+f+g=11 \\ 5+3+f+1=11 \\ f+9=11 \\ f=11-9 \\ f=2 \end{gathered}[/tex]Next:
[tex]\begin{gathered} b+d+e+g=9 \\ 2+d+3+1=9 \\ d+6=9 \\ d=9-6 \\ d=3 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} Total=(a+b+c+g)+d+e+f+h \\ =10+3+3+2+2 \\ =20 \end{gathered}[/tex]The total number of family members is 20.
