[Math] Formula for inverse relationship between ‘scale’ and ‘physical size’

algebra-precalculus

I'm having trouble solving the following problem. Hopefully someone can help!

I have some drawing plans to prepare: the orginal drawing is a scale 1:200 (printed at 100%)

  • if i print at 50% it will be 1:400
  • if i print at 25% it will be 1:800
  • and so on…

I can see there is an inverse relationship between these numbers but i can't at all remember how to express that as a formula.

What would the '%' be for a given scale '1:n'? Can you please also explain how to figure this out?

Thanks!

Best Answer

Your scale would be $1:\frac{200}{\text{print percentage expressed as a decimal}}$, where 50%=0.5, 25%=0.25, etc. Or given the scale, the print percent is $\frac{200}{\text{scale}}$ again expressed as a decimal.

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