Question

In a class, the total numbers of boys and girls are in the ratio 4:3. on one day it was found that 8 boys and 14 girls were absent from the class, and that the number of boys was the square of the number of girls. what is the total number of students in the class?

Answer 1

Let the number of boys and girls in the class be 4x and 3x.
Given,
$4x - 8 = {(3x - 14)}^{2} \\ 4x - 8 = 9 {x}^{2} - 84x + 196 \\ 9 {x}^{2} - 88x + 204 = 0 \\ x = \frac{88 \: + \: \: or \: \: - \sqrt{ {( - 88)}^{2} - 4 \times 9 \times 204} }{2 \times 9} \\ x = \frac{88 \: + \: \: or \: \: - 20}{18} = 6 \: \: or \: \: 3.77$
Only integer value for x is acceptable.
So, x = 6.
Total number of students = 4×6 + 3×6 = 42

Answer 2

Step-by-step explanation:

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