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Ratio Resolution (Posted on 2011-06-15) Difficulty: 2 of 5
Each of x, y and z is a positive real number.

Determine the ratio x:y:z in each of the following equations.

(I) (x+z)/y = z/x = x/(z-y)

(II) 21(x2 + y2 + z2) = (x + 2y + 4z)2

No Solution Yet Submitted by K Sengupta    
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Some Thoughts One way to do part 1 | Comment 2 of 6 |

One way of doing part 1 is to assume, say, z is 1, and see what the other variables come out to:

(x+1)/y = 1/x

x^2 + x = y

we're also given 1/x = x/(1-y)

x^2 = 1-y

then substituting,

1 - y + x = y

x = 2y - 1

Then, substituting again,

2y/y = 1/x

1/x = 2

x = 1/2

then

y = 1/4 + 1/2 = 3/4

Summarizing:

x = 2/4; y = 3/4; z = 4/4

The ratio is 2:3:4.


  Posted by Charlie on 2011-06-15 14:26:17
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