Question

The denominator of a fraction is 3 more than its numerator.

When 1/2 is added to this fraction, the resulting fraction's denominator is twice the denominator of the original fractions and its numerator is 1 more than its denominator.

What is the numerator of the original fraction?

Answer 1

Numerator of the original fraction is 1

Explanation:

Let's assume numerator of fraction as 'y'

denominator of fraction as 'x'

so, fraction is

`(y)/(x)`

The denominator of a fraction is 3 more than its numerator

so,
`x=y+3`

When 1/2 is added to this fraction, the resulting fraction's denominator is twice the denominator of the original fractions and its numerator is 1 more than its denominator

so,

`(y)/(x)+(1)/(2)=(x+1)/(2x)`

we can use first equation and plug x

`(y)/(y+3)+(1)/(2)=(y+3+1)/(2(y+3))`

now, we can solve for y

we get

`(y)/(y+3)\cdot \:2\left(y+3\right)+(1)/(2)\cdot \:2\left(y+3\right)=(y+4)/(2\left(y+3\right))\cdot \:2\left(y+3\right)`

`3y+3=y+4`

`2y=1`

`y=(1)/(2)`

now, we can find x

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

`x=(7)/(2)`

now, we can find fraction

`(y)/(x)=((1)/(2) )/((7)/(2))`

`(y)/(x) =(1)/(7)`

So,

Numerator is 1