Class of 20 students, 13 play soccer, 8 play tennis and 2 play neither.
Find how many students
a) Play soccer or tennis
b) Play both soccer and tennis
c) Play only soccer
made a Venn diagram, labeled the intersection of the soccer circle and the tennis circle as x
then ...
13-x + x - 8-x + 2 = 20
-x = -3
x = 3
All can now be seen from the Venn diagram
soccer of tennis --- 18
both soccer and tennis -- 3
only soccer --- 10
y6
To find the number of students who play soccer or tennis, we need to add the number of students who play soccer and the number of students who play tennis. However, we need to subtract the number of students who play both soccer and tennis as they would be counted twice.
a) Play soccer or tennis:
Total number of students - number of students who play neither = (20 - 2) = 18
b) Play both soccer and tennis:
Number of students who play soccer + number of students who play tennis - number of students who play both soccer and tennis = (13 + 8 - 2) = 19
c) Play only soccer:
Number of students who play soccer - number of students who play both soccer and tennis = (13 - 2) = 11
To find the number of students who play soccer or tennis, you need to add the number of students who play soccer to the number of students who play tennis. However, you need to account for the students who play both soccer and tennis, as they would be counted twice if you simply added the two numbers together.
To find the number of students who play both soccer and tennis, you need to find the intersection between the two groups. This means you need to find the number of students who are in both the soccer-playing group and the tennis-playing group.
To find the number of students who play only soccer, you need to subtract the number of students who play both soccer and tennis from the total number of soccer players.
Now, let's calculate the answers:
a) Play soccer or tennis:
First, find the number of students who play both soccer and tennis: 13 (soccer players) + 8 (tennis players) - 2 (both soccer and tennis) = 19.
So, 19 students play soccer or tennis.
b) Play both soccer and tennis:
This is already calculated in the previous step. There are 2 students who play both soccer and tennis.
c) Play only soccer:
To calculate the number of students who play only soccer, subtract the number of students who play both soccer and tennis from the total number of soccer players: 13 (soccer players) - 2 (both soccer and tennis) = 11.
Therefore, 11 students play only soccer.