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I have a scale which goes from 0 to 100. Given a number on that scale (say 33) I want to find the corresponding value on another scale which goes from 25 to 100 (in this case I think the answer is 50).

Any ideas how I should go about working out the equation to calculate what the corresponding value is on the 2nd scale? enter image description here

richwol
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2 Answers2

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Assuming you want a linear transformation, you need to do the following: $$y_{\text{new}}-25=\frac{100-25}{100-0}\,x.$$ Check one: $0$ should go to $25$, which it does. Check two: $100$ should go to $100$, which it does. Check three: the relationship is linear, which it is.

Adrian Keister
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  • Amazing, that's the first time I've used one a linear equation I like that and it really helped me to understand it. Thanks! – richwol Jun 27 '18 at 15:48
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You want a linear equation relating the first scale (call it $x$) with the second scale (call it $y$). The line goes through the two points $(0,25)$ and $(100,100)$. Can you use that information to find the equation of the line?

rogerl
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