Question

If someone could help me answer this and possibly give me a step-by-step for future reference that'd be great thanks.

Answer 1

Answer:

Let's look at the Venn diagram and the data we have:

There are 12 pupils

9 have a brother

7 have a sister

2 have neither.

Now let's look at the diagram.

We know that the circle B represents the pupils who have a brother

Circle S represents the students that have a sister.

Then the intersection of the circles, represents the number of students that have both.

And the space outside the circles represents the pupils that do not have a brother nor a sister.

Then the first thing we can complete is a 2 in the bottom left corner, because we already know that there are 2 pupils that do not have brothers nor sisters.

Now let's find the number of students that have both, brothers and sisters:

There are 12 pupils.

9 have a brother

7 have a sister

2 have neither

if we add that, we get:

9 + 7 + 2 = 18

This is larger than 12, this means that we are counting some of the students more than once.

If X is the number of students that we are counting twice, we should have:

18 - X  = 12

18 -12 = X = 6

There are 6 students who we are counting twice, and this happens because these 6 students have a brother and a sister.

Then in the intersection of both circles we should put a 6.

At the left of that (in the part that we have only circle B) we need to write the number of students that only have a brother, this is the number of students that have a brother minus the number of pupils that have a brother and a sister, this is:

9 - 6 = 3

We need to write a 3 in that square.

And in the last square (the one that is only one circle S) we need to write the number of pupils that only have a sister, this is calculated in the same way than before, this is:

7 - 6 = 1

We need to write a 1 in the rightmost square.