In a senior secondary school, 80 students play hockey or football. The number that play football is 5 more than twice the number that play hockey. If the 15 students play both games and every student in the school playsat least one game, find:
The number of students that play football;
The number of students that play football but not hockey;
The number of students that play hockey but not football. Full working sir
Start with a Venn diagram.
The intersection is 15, and the total population is 80
Set up the expressions that relate hockey and football.
Set up the equation for all of the students added together...
Solve : )
Review your Venn diagram stuff. If
f play only football
h play only hockey,
then we have
h+f-15 = 80
f+15 = 5+2(h+15)
Now just solve for f and h, and you can answer the questions.
To get the number that play football but not hockey is that you will subtract 65 from 15
To get hockey but not football is that you will subtract 65 from 50 then you will subtract the intersect from your answer.
To solve this problem, we'll use a system of equations. Let's assign variables to the unknowns:
Let's say the number of students that play hockey is "x".
Therefore, the number of students that play football is "2x + 5" (5 more than twice the number that play hockey).
We are given that 80 students play hockey or football in total. So, the sum of students playing hockey and football is 80:
x + (2x + 5) = 80
Simplifying the equation:
3x + 5 = 80
Subtracting 5 from both sides of the equation:
3x = 75
Dividing both sides by 3:
x = 25
Now we have found that the number of students playing hockey is 25. To find the number of students playing football, substitute this value into the equation:
Number of students playing football = 2x + 5 = 2(25) + 5 = 55
Therefore, there are 55 students playing football.
To find the number of students that play football but not hockey, we subtract the number of students playing both games (15) from the total number of students playing football:
Number of students playing football but not hockey = 55 - 15 = 40
Therefore, there are 40 students playing football but not hockey.
To find the number of students playing hockey but not football, we subtract the number of students playing both games (15) from the total number of students playing hockey:
Number of students playing hockey but not football = 25 - 15 = 10
Therefore, there are 10 students playing hockey but not football.