Percentage parts adjustment

Question

I have $3$ variable components that are percentages and $X+Y+Z$ always equals $100$. I cannot seem to find the proper way to calculate $Y$ and $Z$ if I increase $X$ by $25$ for example. I know it is a very stupid question but I am stuck.

Answer 1

If I understand your problem well, you want to find $Y'$ and $Z'$ so that:

• $X'+Y'+Z'=100$

• $\frac{Y}{Z}=\frac{Y'}{Z'}$

assuming $Z\neq 0$ and $X'$ is the new, fixed value of $X$.

Solving this system yields:

$Z' = \frac{100-X'}{\frac{Y}{Z}+1}$ and $Y' = \frac{Y}{Z}Z'$