Question

The denominator of a fraction is 4 less than the numerator. if 3 is added to both nu,erator and denomiator the result is 3/2. find the sum of the numerator and the denominator of the orignal fraction

Answer 1

Let the numerator be x
numerator =x
denominator = x - 4
fraction =
`(x)/(x-4)`

Add 3 to numerator and denomiator
numerator = x + 3
denominator = x -4 + 3 = x - 1
fraction =
`(x+ 3)/(x - 1)`


`(x+ 3)/(x - 1)` =
`(3)/(2)`

cross multiply:
2(x + 3) = 3(x - 1)
2x + 6 = 3x - 3
3x - 2x = 6 + 3
x = 9

Orignal fraction =
`(x)/(x -4)`
=
`(9)/(9-4)`
=
`(9)/(5)`

Sum of the numerator and denominator = 9 + 5 = 14