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(D) Let the number of children be $x$.Each child receives $\frac{120}{x}$ kites.If there are $4$ children fewer,the number of children is $(x - 4)$.In

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(D) Let the number of children be $x$.Each child receives $\frac{120}{x}$ kites.If there are $4$ children fewer,the number of children is $(x - 4)$.In this case,each child receives $\frac{120}{x - 4}$ kites.According to the problem,$\frac{120}{x - 4} - \frac{120}{x} = 1$.Multiplying by $x(x - 4)$,we get $120x - 120(x - 4) = x(x - 4)$.$120x - 120x + 480 = x^2 - 4x$.$x^2 - 4x - 480 = 0$.Factoring the quadratic equation: $(x - 24)(x + 20) = 0$.Since the number of children cannot be negative,$x = 24$.

$120$ kites were divided equally among a certain number of children in a school. If there were $4$ children fewer,each child would have received $1$ kite more. Find the number of children.

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