Question

Given (3x-y):(6x+2y)=3:14,find x:y

Answer 1

`x:y=5:6`

Explanation:

The given equation is

`(3x-y):(6x+2y)=3:14`

We change the ratios into fractions to obtain;

`((3x-y))/(6x+2y)=(3)/(14)`

We cross multiply to obtain;

`14(3x-y)=3(6x+2y)`

We expand the brackets to obtain;

`42x-14y=18x+6y`

We group similar terms to obtain;

`42x-18x=6y+14y`

Simplify;

`24x=20y`

Divide both sides by
`24y` to obtain;

`(24x)/(24y)=(20y)/(24y)`

This implies that;

`(x)/(y)=(5)/(6)`

Therefore

`x:y=5:6`

Answer 2

`(x)/(y)=(5)/(6)`

Explanation:

we have

`(3x-y)/(6x+2y)=(3)/(14)`

Multiply in cross

`(3x-y)/(6x+2y)=(3)/(14)\\ \\3(6x+2y)=14( 3x-y)\\ \\18x+6y=42x-14y\\ \\42x-18x=6y+14y\\ \\24x=20y\\ \\(x)/(y)=(20)/(24)\\ \\(x)/(y)=(5)/(6)`