Question

Three eighth of the students of a class opted for visiting an old age home. Sixteen students opted for having a nature walk. Square root of total number of students in the class opted for tree plantation in the school. The number of students who visited an old age home is same as the number of students who went for a nature walk and did tree plantation. Find the total number of student. What values are inculcated in students through such activities?

Answer 1

Let the total number of students = x
Number of students who visited old age home =$\frac{3x}{8}$
Number of students who went for nature walk = 16
Number of students who opte for tree plantation = 
According to question 
$\frac{3x}{8}$ = 16 + $\sqrt{x}$
$\frac{3x}{8}$ - 16 = $\sqrt{x}$

3x - 128 = 8 $\sqrt{x}$
(3x - 128)² = 64x
9x² + 16384 - 768x = 64x
9x² - 832x + 16384 = 0
9x² - 576x - 256x + 16384 = 0
9x(x - 64) - 256(x - 64) = 0
(x - 64)(9x - 256) = 0
x - 64 = 0 or 9x - 256 = 0
x = 64 or x = $\frac{256}{9}$ (neglected)
So, total number of students = 64

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Answer 2

Answer:

x = 64 students

Step-by-step explanation:

Let the total number of students = x

Number of students who visited old age home =3x/8

Number of students who went for nature walk = 16

Number of students who opte for tree plantation =

According to question

3x/8 = 16 + √x

3x/8- 16 = √x

3x - 128 = 8 √x

(3x - 128)² = 64x

9x² + 16384 - 768x = 64x

9x² - 832x + 16384 = 0

9x² - 576x - 256x + 16384 = 0

9x(x - 64) - 256(x - 64) = 0

(x - 64)(9x - 256) = 0

x - 64 = 0 or 9x - 256 = 0

x = 64 or x = 256/9 (neglected)

So, total number of students = 64