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.
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.
To solve this problem, let's break it down step by step:
1) Let's assume the number of students playing hockey is "x". So, the number of students playing football would be 2x + 5 (as it is stated that the number playing football is 5 more than twice the number playing hockey).
2) We are given that 15 students play both games. So, we need to subtract this number from the total number of football players to find the number of students playing football but not hockey.
3) Similarly, we need to subtract the number of students playing both games from the total number of hockey players to find the number of students playing hockey but not football.
Let's calculate each answer step by step:
1) The number of students playing football:
Total number of students playing hockey + Total number of students playing football = 180
x + (2x + 5) = 180
3x + 5 = 180
3x = 180 - 5
3x = 175
x = 175 / 3
x ≈ 58.33 (rounded to the nearest whole number)
So, approximately 58 students play hockey.
To find the number of students playing football:
2x + 5 = 2(58) + 5
= 116 + 5
= 121
Therefore, 121 students play football.
2) The number of students playing football but not hockey:
121 - 15 (students playing both games) = 106 students play football only.
3) The number of students playing hockey but not football:
58 - 15 (students playing both games) = 43 students play hockey only.
In summary:
1) The number of students that play football: 121
2) The number of students that play football but not hockey: 106
3) The number of students that play hockey but not football: 43