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ratio - mixed answers?

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That's a really weird way to pose a math problem. Hope I can clarify this a bit more:
If you express the answer as a ratio, you basically can set one of the variables to any value. For the sake of argument, let z = 1.  
If 6y = 5z, then y = ⅚z. If z = 1, then y = 5/6.  
Same with 10x = 7z -> x = 7/10  
The right ratio would be  

7/10 : 5/6 : 1  

You can multiple by 30 to have an integer answer  

21 : 25 : 30  

Edit: you can also just invert the numbers you have. If 50x = 42y = 35z then the ratio is 1/50 : 1/42 : 1/35, multiplying everything by 1050 it's still 21 : 25 : 30
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If the equation was 1x = 2y the ratio would not be 1:2. It would be 2:1 as x is the bigger value.
by
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It is. That's the most reduced form. Who is telling you otherwise?

Edit: Apologies. The 10x = 7z, instead of y.

Multiply the first equation by 5, and the second equation by 7. Then simplify.

 My apologies, I dont know how I misread that the first time

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