In a senior secondary school iti student played hockey or football the number that play football is five more than twice the number that played hockey if 15 students play the both game and every student in the school please at least one game find the number of students that play football the number of student that played football but not hockey the number of students that played hockey but not football
Let the number of students that played hockey be H and the number of students that played football be F.
Given that the number of students that played football is five more than twice the number that played hockey, we can write the equation:
F = 2H + 5
We also know that 15 students played both games, so the total number of students playing hockey or football is H + F - 15.
Since every student in the school plays at least one game, this total number of students must be equal to the total number of students in the school.
Let S be the total number of students in the school.
Thus, we have the equation:
H + F - 15 = S
Now, we need to find the values of F, H, and the number of students that played football but not hockey.
To do this, we can rearrange the equation F = 2H + 5 and substitute it into the equation H + F - 15 = S:
H + (2H + 5) - 15 = S
Combining like terms:
3H - 10 = S
Therefore, the number of students that played hockey is (S + 10) / 3.
Now that we know H, we can substitute it back into the equation F = 2H + 5 to find the number of students that played football:
F = 2((S + 10) / 3) + 5
Finally, to find the number of students that played football but not hockey, we subtract the number of students that played both games from the total number of students that played football:
Number of students that played football but not hockey = F - 15