Question

The sum of the numerator and the denominator of a rational number is 19. If 3 is added to the numerator the rational number becomes 1/3 What is the rational number?​

Answer 1

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The sum of the numerator and the denominator of a rational number is 19. If 3 is added to the numerator the rational number becomes 1/3 What is the rational number?

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$let \: the \: numarator \: be \: = x$

$let \: the \: denominator \: be \: = 19 - x$

$according \: to \: the \: question$

$\frac{x + 3}{19 - x} = \frac{1}{3}$

$3(x + 3) = 19 - x$

$3x + 9 = 19 - x$

$3x + x = 19 - 9$

$4x = 10$

$x = \frac{10}{4}$

$x = 2.5$

$numerator \: is \: x \: = \: 2.5$

$(denominator \: is \: 19 - x = 19 - 2.5)$

$denominator = 16.5$

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