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The number of those who attended the picnic was 8.
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = = 0 where a, b, c, ∈ R and a ≠ 0.
Such questions are best examples of quadratic equations where the unknown is simply assumed to be a variable which when substituted according to the conditions yield a quadratic equation which can easily be solved.
Let x represent the whole population.
Total Spending = Rs. 96
Thus, each individual's contribution is equal to 96/x.
Four people did not show up causing
others to contribute Rs. 4 extra.
So the given condition can be written as
96/(x-4) – 96/x = 4
=>96x – 96(x-4) = 4x(x-4)
=> 96x -96x + 384 = 4x2 – 16x
=> 4x2 – 16x – 384 = 0
=> x2 – 4x – 96 = 0
=> (x – 12)(x + 8) = 0
=> x = 12 or x = -8 (neglect)
So x = 12
x-4 = 8 ( because four of them did not turn up)
∴ The number of those who attended the picnic was 8.
Learn more about quadratic equations here :
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