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If something cost x, what is the cost of something 3.5 times lower cost?

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Pretend the cost is $20, so x=20.
Divide both sides by the proportion it will lowered.  If it was 2 times lower cost, divide both sides by 2.
That's the format you should follow using whatever value you would like.  The important part isn't the $10, as it will work for any value you choose.  


3.5 isn't a proportion.  As I understand your logic something at .50% lower cost (.5 times lower cost) would cost twice as much, right?  Using your x=$20 you suggest dividing both sides by .5, so x/.5=20/.5=$40.
Sorry, proportion was not a good word to use, I think scale is better.
If the cost is $20, I would imagine something 2 times lower cost would be x/2.  You can call it 50% lower cost, but then you would multiply by .5, not divide.  So x/2=.5x=$10. 
So, if something was 3.5 lower cost, I would assume you mean x/3.5.
So x costs $35, something else 3.5 lower cost is 35/3.5, or $10.
Thanks Michael, I imagine that you are correct in what was meant but I am trying to determine what the actual answer is rather than what we might imagine was intended.  Perhaps I really need an English teacher, eh?