Question

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​

Answer 1

Answer:

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