Question

The numerator of a fraction is 3 less than the denominator. If 5 is added to the numerator and the denominator, the value of the resulting fraction becomes 3/4. What is the original fraction?

Answer 1

x = Denominator

nominator = x - 3


( x - 3 + 5 ) / ( x + 5 ) = 3 / 4

( x + 2 ) / ( x + 5 ) = 3 / 4

4 ( x + 2 ) = 3 ( x + 5 )

4 x + 8 = 3 x + 15

4 x - 3 x = 15 - 8

x = 7


Denominator = 7

The numerator is 3 less than the denominator.

Numerator = 7 - 3 = 4


original fraction = 4 /7


Proof :

( 4 + 5 ) / ( 7 + 5 ) = 9 / 12 = 3 * 3 / ( 3 * 4 ) = 3 / 4