Converting between different scales

Question

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?

Answer 1

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.

Answer 2

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?