In a class, one third of students had gone to watch drama. Twice the square root of the students had gone to watch magic show and remaining 12 students had gone to watch football match. Find the total number of students in the class.
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Answered by
67
Let the total number of students in Class be X
Thus according to question
Student went to drama = A = X/3
Student went to magic show =B = 2 root X
Student went to football = C = 12
Thus
X= X/3 + 2 root X + 12
2X/3 = 2 root X + 12
2 root X= 2X/3 - 12
Squaring both sides
4X = 4X^2/9 + 144 - 48X/3
4X^2/9 - 60X/3 + 144 = 0
4X^2/9 - 20X + 144 = 0
4X^2 - 180X + 1296 = 0
X^2 - 45X + 324 = 0
X^2 - 36X - 9X + 324 = 0
X(X - 36) - 9 (X-36) = 0
X = 36
thus total Students = 36
Thus according to question
Student went to drama = A = X/3
Student went to magic show =B = 2 root X
Student went to football = C = 12
Thus
X= X/3 + 2 root X + 12
2X/3 = 2 root X + 12
2 root X= 2X/3 - 12
Squaring both sides
4X = 4X^2/9 + 144 - 48X/3
4X^2/9 - 60X/3 + 144 = 0
4X^2/9 - 20X + 144 = 0
4X^2 - 180X + 1296 = 0
X^2 - 45X + 324 = 0
X^2 - 36X - 9X + 324 = 0
X(X - 36) - 9 (X-36) = 0
X = 36
thus total Students = 36
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25
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