Solve Ratio of x:y:z for y/(x-z)=(y+x)/z=x/y

[Miike012]

Homework Statement

IF y/(x-z) = (y+x)/z = x/y
Find the ratio of x:y:z

My thoughts: I have to get y/(x-z) = (y+x)/z = x/y to have the ratio x:y:z somehow then solve...?

The Attempt at a Solution

 

[ehild]

Try the equations

y/(x-z)=x/y and (y+x)/z=x/y.

Solve for y and z in terms of x.

ehild

 

[Miike012]

Algebra Prob.. Help please.

Homework Statement

The question is...
If y/(x-z) = (x+y)/z = x/z,
Find the ratios of x:y:z.

Here is the website that has the solution to the problem, But I am not understanding the solution because they are leaving information out.
http://www.mathh3lp.webs.com/

1) How did they determine that the ratio is 2 just by adding the three?
2)How did they get to (x+y)/z = x/y = 2.
3) How did they get to y = -x, and y/(x-z) = x/y ?

 

[ehild]

Try to solve the problem yourself. See my answer to your previous thread about the same problem.

ehild

 

[Miike012]

I can't find the post...
I think you said...
y/(x-z) = x/y
(x+y)/z = x/y
And solve?

 

[berkeman]

I can't find the post...
I think you said...
y/(x-z) = x/y
(x+y)/z = x/y
And solve?

(I merged your two threads for you)

 

[eumyang]

1) How did they determine that the ratio is 2 just by adding the three?

Consider three equivalent fractions, like
1/3, 2/6, and 3/9.
Find $$\frac{the.sum.of.the.numerators}{the.sum.of.the.denominators}$$ . What can you say about the resulting fraction?

2)How did they get to (x+y)/z = x/y = 2.

Since it was determined that each ratio is equal to 2 (or 2:1), it was written out that
ratio #2 = ratio #3 = 2 in order to determine the ratio for x:y:z.

3) How did they get to y = -x, and y/(x-z) = x/y ?

Two cases were considered here. In the first case, x + y ≠ 0. In the second case, x + y = 0, or y = -x. Simple, really.