Question

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 15 students play both games and every student in the school plays at least one game with the aid of using venn diagram :the number of students that play football

Answer 1

Let's assign variables to the different quantities mentioned in the problem:
Let h = number of students that play hockey
Let f = number of students that play football

We are given that 80 students play hockey or football, so we can write the equation:
h + f = 80 (Equation 1)

We are also given that the number of students that play football is 5 more than twice the number that play hockey, so we can write the equation:
f = 2h + 5 (Equation 2)

We are also given that 15 students play both games, so we can write the equation:
f + h - 15 = 80 (Equation 3) (This accounts for the overlap between football and hockey players)

Now, we can use these equations to solve for the number of students that play football.

From Equation 1, we can express h in terms of f:
h = 80 - f

Substituting this into Equations 2 and 3, we have:
f = 2h + 5
f = 2(80 - f) + 5
f = 160 - 2f + 5
3f = 165
f = 55

Therefore, the number of students that play football is 55.

Answer 2

Show it with Venn diagram

Answer 3

Apologies for the confusion. Here is how the Venn diagram should look like based on the given information:

The left circle represents hockey players, the right circle represents football players, and the overlapping region represents students who play both hockey and football.

Label the left circle as "Hockey" and write "h" inside it, to represent the number of students playing hockey.
Label the right circle as "Football" and write "f" inside it, to represent the number of students playing football.

In the overlapping region, write "15" to represent the number of students playing both hockey and football.

Now, we know that the total number of students who play hockey or football is 80. So, write "80" outside the circles to represent the total number of students.

To find the number of students playing football, we need to determine the value of "f". To do this, we will use the given information that the number of students playing football is 5 more than twice the number playing hockey.

Let's say there are 30 students playing hockey (h=30).
Using the given information, we can calculate the number of students playing football:
f = 2h + 5 = 2(30) + 5 = 60 + 5 = 65.

So, we now know that there are 65 students playing football.

In the Venn diagram, you can write "65" inside the Football circle to indicate the number of students playing football.

This Venn diagram represents the given information and visually represents the number of students playing hockey and football.