Question

If x (x+y) = 27 and y (x+y) = 54, what is the value of (x+y)^2?

Answer 1

If x=27 and y=54, add them together then multiply by 2 and get 162

Answer 2

9x^2

Explanation:

It is given that:

x ( x + y ) = 27

If one manipulates the equation, by dividing by x, they get:

x + y = 27/x

It is also given that:

y ( x + y ) = 54

Again, manipulate the equation, only this time, divide by y,

x + y = 54/y

It is obvious that;

x + y = x + y

Yet this was proven;

x + y = 27/x

x + y = 54/y

Therefore, the following has to be true;

27/x = 54/y

To sove the proportion, use cross products;

27/x = 54/y

54x = 27y

Inverse operations:

54x = 27y

/27 /27

y = 2x

Substitute;

(x + y)

y = 2x

= (x + 2x)

= 3x

Now solve:

(3x)^2

9x^2