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In a senior secondary school,80 students play football or hockey.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 (i)the number of students that play football (ii)the number of students that play football but not hockey (iii)the number of students that play hockey but not football.

Monjur Alahi

In a senior secondary school,80 students play football or hockey. The number that plays football is 5 more than twice the number that plays hockey. If 15 students play both games and every student in the school plays at least one game, find (i)the number of students that play football (ii)the number of students that play football but not hockey (iii)the number of students that play hockey but not football. It 


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2 Answers

Salim Ahmed Kawsar

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I thought F or H = 80 is giving by
n(F u H) = n(F) + n(H) - n(F n H)

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Salim Ahmed Kawsar

Call

Let the no of students who play hockey = x

No of students who play football = 2x + 5

No of students who play both hockey and football = 15

ATQ,

x + 2x + 5 -15 = 80

3x - 10 = 80

3x = 90 ∴ x = 30

No of students who play football = 2 × 30 + 5 = 65

Hence, 30 students play hockey, 65 play football and 15 play both.

(i) 65 students play football

(ii) No of students who play football but not hockey = 65 - 15 = 50

(iii) No. of students who play hockey but not football. = 30 - 15 = 15

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