the denominator of a rational number is greater than numerator by 7 .if 3 is subtracted from the numerator and 2 is added to its to its denominator,the new number becomes 1/5. find rational number
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Fraction = \dfrac{x}{x+7}
x+7
x
Given that if 3 is subtracted from the numerator and 2 is added to its denominator , the new number becomes 1/5
As numerator was x, 3 subtracted from numerator = ( x - 3 )
As denominator was x + 7 , 2 added to denominator = ( x + 7 + 2 )
= x + 9
New fraction =\dfrac{x-3}{x+9}
x+9
x−3
According to the question, new fraction is equal to 1 / 5.
1 / 5 = ( x - 3 ) / ( x + 9 )
x + 9 = 5( x - 3 )
x + 9 = 5x - 15
9 + 15 = 5x - x
24 = 4x
24 / 4 = x
6 = x
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