Question

I am thinking of a fraction. The sum of the numerator and denominator is 19. When I add

8 to the denominator, the fraction becomes 1/2 What is the fraction I am thinking of?​

Answer 1

`(9)/(10)`

Explanation:

Let the fraction be
`(x)/(y)`.

That would mean:

(1) x+y = 19

&

(2) y+8 = 2x or 2x = y+8

In order to use substitution, we multiply equation by 2:

(3) 2x+2y = 38

Then we substitute equation (2) into (3):

y+8 + 2y = 38

3y + 8 = 38

3y = 30

y = 10

Substitute this into equation (1)

x + 10 = 19

x = 9

Therefore the fraction would be:

`(9)/(10)`

Answer 2

9/10

Explanation:

let the fraction be x/y.

x+y=19

x/y+8=1/2

solve simultaneously

y=2x-8

y=19-x

2x-8=19-x

3x=27

x=9

y=10