Question

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)the number of students that play hockey but not football.

Answer 1

Number that play hockey --- x
number that play football --- 2x+5
number that play both = 15
number that play hockey only = x-15
number that play football only = 2x+5 - 15 = 2x - 10

only football + only hockey + both = 180
x-15 + 2x-10 + 15 = 180
3x = 190
x = not a whole number.
Your data appears to be inconsistent.

2nd approach:

let the number of only hockey be h
let the number of only football be f
h+f+15 = 180
h+f = 165 **

f+15 = 2(h+15) + 5
f + 15 = 2h + 35
f - 2h = 20 ***

subtract *** from **
3h = 145
h = 145/3 , same conclusion as above

btw, if you check, my two solutions are consistent.