The problem seems to be incomplete, since we are missing the question we are supposed to answer. The complete problem should look something like this:
In a survey asking students whether they have brothers and/or sisters, the results determined all of the following statements to be true for the group: 24 students had a brother(s) 27 students had a sister(s) 10 students had both a brother(s) and a sister(s) 6 students had no siblings
How many students were surveyed for this study?
Answer:
47
Step-by-step explanation:
This problem can be solved by making use of a Venn Diagram (See attached picture).
In the ven diagram we can see two circles that will represent different sets. The first circle tagged B will represent the students that have one or more brothers. The second circle tagged S represents the set of students that have one or more sisters. Everything outside of the circles will contain the students that don't have a brother or a sister. The region where the two circles cross each other will contain the students that have both brothers and sisters.
So we start by filling this center space with the number of students that have both brothers and sisters: 10.
Once we filled this section we can start filling the rest. We know that 24 students had brothers. This group of 24 students will include the group of students that have both brothers and sisters so we need to subtract these 10 students from the 24 to get the number of students that will only have brothers:
24-10=14
so we can go ahead and write the 14 in the brothers circle.
The same is done for the sisters circle:
27-10=17
which means that 17 of the surveyed students had only a sister or sisters, so we go ahead and write that 17 in the S circle.
and finally the problem tells us that only 6 students will have no siblings so we write that number outside of the circle.
So now that the Venn diagram is filled we can add all the values together to get the total number of students that were surveyed:
6+14+10+17=47
