in a school,180 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,find:1) the number of students that play football.2)the number of students that play football but not hockey.3)thr number of students that play hockey but not football

h + 2h+5 - 15 = 180

3h = 190
Hmmm. h must be an integer. I suspect a typo

63+131-15 = 179
64+133-15 = 182

To solve this problem, let's denote the number of students playing hockey as 'x' and the number of students playing football as 'y'.

1) The number of students that play football:
Given that the total number of students playing both sports (hockey and football) is 15, we can set up the equation:

x + y - 15 = 180

Now, we know that the number of students playing football is 5 more than twice the number playing hockey. So, we can write another equation:

y = 2x + 5

We can solve this system of equations to find the values of x and y:

x + y - 15 = 180
y = 2x + 5

Rearranging the first equation, we get:

x + y = 180 + 15
x + y = 195

Substituting the value of y from the second equation into the first equation:

x + (2x + 5) = 195
3x + 5 = 195
3x = 195 - 5
3x = 190
x = 190 / 3
x = 63

Now, plugging this value of x into the second equation:

y = 2(63) + 5
y = 126 + 5
y = 131

Therefore, the number of students that play football (y) is 131.

2) The number of students that play football but not hockey:
To find this value, we need to subtract the number of students playing both games (15) from the total number of students playing football (131):

131 - 15 = 116

Therefore, the number of students that play football but not hockey is 116.

3) The number of students that play hockey but not football:
To find this value, we subtract the number of students playing both games (15) from the total number of students playing hockey (63):

63 - 15 = 48

Therefore, the number of students that play hockey but not football is 48.

To solve this problem, let's break it down step by step:

1) Let's assume the number of students playing hockey is 'x'.
According to the problem, the number of students playing football is 5 more than twice the number of students playing hockey.
Therefore, the number of students playing football can be determined as 2x + 5.

2) We know that 15 students play both hockey and football.
So, to find the number of students playing only football (not hockey), we need to subtract the number of students playing both games (15) from the total number of students playing football.
Therefore, the number of students playing football but not hockey is (2x + 5) - 15.

3) Similarly, to find the number of students playing only hockey (not football), we need to subtract the number of students playing both games (15) from the total number of students playing hockey.
Therefore, the number of students playing hockey but not football is x - 15.

Please note that to find the actual values of these quantities, we need to know the value of 'x' (the number of students playing hockey).