Question

the numerator of a fraction is 4 less than the denominator if 7 is added to each numerator and denominator the fraction becomes 2/3 find the fraction

Answer 1

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SOLUTION:

$let \: the \: fraction \: be \: \frac{x}{y} \\then \: according \: to \: question \\ x = y - 4 \: \: and \: \: \frac{x + 7}{y + 7} = \frac{2}{3} \\ performing \: simplification \: \\ we \: get \\ \\ - x + y = 4(eq {}^{1} )\: \: \: and \: \: 3x - 2y = - 7(eq {}^{2}) \\ \\ multiply \: both \: sides \: of \: eq {}^{1} with \: 3 \\ = > - 3x + 3y = 12(eq {}^{3} ) \\ \\ now \: add \: eq {}^{2} and \: eq {}^{3} \\ = > y = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (simple \: addition) \\ \\ put \: \: y = 5 \: in \: eq {}^{1} \\ \\ we \: get \\ - x + 5 = 4 \\ = > x = 1$

THEREFORE THE FRACTION IS

1/5

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Answer 2

REQUIRED FRACTION => 1/5

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