Question

I am equivalent to 2/3. The sum of my numerator and my denominator is 30. The difference between my denominator and my numerator is 6. What fraction am i?.

Answer 1

`(12)/(18)`

Explanation:

let the original fraction be

`(x)/(y)`

then

x + y = 30 → (1)

y - x = 6 , that is

- x + y = 6 → (2)

add (1) and (2) term by term to eliminate x

0 + 2y = 36

2y = 36 ( divide both sides by 2 )

y = 18

substitute y = 18 into (1) and solve for x

x + 18 = 30 ( subtract 18 from both sides )

x = 12

then the original fraction is

`(x)/(y)` =
`(12)/(18)`