A fraction becomes $\frac{1}{2}$ if 5 is subtracted from its numerator and 3 is subtracted from its denominator. If the denominator of this fraction is 5 more than its numerator, find the fraction.

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Solution

Let fraction $= \frac{x}{y}$
$fraction numerator x minus 5 over denominator y minus 3 end fraction equals 1 half$

$2 x - 10 = y - 3 2 x - y = 7 - - - - (1) a n d y = x + 5$

put this in (1)

$2x−(x+5)=72x−x−5=7x=7+5x=12y=x+5y=12+5=17fraction=1217$

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A fraction becomes 12 if 5 is subtracted from its numerator and 3 is subtracted from its denominator. If the denominator of this fraction is 5 more than its numerator, find the fraction.

Let fraction =xy 2x−10=y−32x−y=7−−−−(1)and y=x+5 put this in (1) 2x−(x+5)=72x−x−5=7x=7+5x=12y=x+5y=12+5=17fraction=1217

A fraction becomes $\frac{1}{2}$ if 5 is subtracted from its numerator and 3 is subtracted from its denominator. If the denominator of this fraction is 5 more than its numerator, find the fraction.

Let fraction $= \frac{x}{y}$
$fraction numerator x minus 5 over denominator y minus 3 end fraction equals 1 half$

$2 x - 10 = y - 3 2 x - y = 7 - - - - (1) a n d y = x + 5$

put this in (1)

$2x−(x+5)=72x−x−5=7x=7+5x=12y=x+5y=12+5=17fraction=1217$