Question

Show that x + y : x - y= 3 : 2

Answer 1

x + y : x - y = (5/2+1/2) : (5/2-1/2)

x + y : x - y = 3 : 2

Therefore, x + y : x - y= 3 : 2 is proved.

Explanation:

Given

x + y : x - y = 3 : 2

As

`x + y = 3`

`x - y = 2`

Solving to find x and y

`\begin{bmatrix}x+y=3\\ x-y=2\end{bmatrix}`

`x-y=2`

`-`

`\underline{x+y=3}`

`-2y=-1`

`\begin{bmatrix}x+y=3\\ -2y=-1\end{bmatrix}`

solve for y

`-2y=-1`

Divide both sides by 2

`(-2y)/(-2)=(-1)/(-2)`

`y=(1)/(2)`

`\mathrm{For\:}x+y=3\mathrm{\:plug\:in\:}y=(1)/(2)`

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

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

`x=(5)/(2)`

so

`x=(5)/(2),\:y=(1)/(2)`

Thus,

x + y : x - y = (5/2+1/2) : (5/2-1/2)

x + y : x - y = 3 : 2

Therefore, x + y : x - y= 3 : 2 is proved.