Dverview
1
2
3
8
9
10
11
12
Question Progress
$1 / 3$ Marks
Homework Progress
$18 / 39$ Marks
In a group of 30 people,
12 have a sister
15 have a brother
11 do not have a sister nor a brother
Complete the Venn diagram to show this information.
$\xi=$ group of 30 people.
$\mathrm{S}=$ people who have a sister.
$B=$ people who have a brother.
Answer
\(\boxed{8}\) people have both a sister and a brother, \(\boxed{4}\) people have only a sister, \(\boxed{7}\) people have only a brother, and \(\boxed{11}\) people have neither a sister nor a brother.
Step 1 ：Let A be the number of people who have both a sister and a brother, S_only be the number of people who have only a sister, and B_only be the number of people who have only a brother.
Step 2 ：We know that \(A + S_{only} = 12\), \(A + B_{only} = 15\), and \(A + S_{only} + B_{only} + 11 = 30\).
Step 3 ：Solving these equations, we find that \(A = 8\), \(S_{only} = 4\), and \(B_{only} = 7\).
Step 4 ：\(\boxed{8}\) people have both a sister and a brother, \(\boxed{4}\) people have only a sister, \(\boxed{7}\) people have only a brother, and \(\boxed{11}\) people have neither a sister nor a brother.
