Artificial intelligent assistant

Proportionally decrease 3 numbers by n percent I have 3 numbers 5, 90, 60, that gives = 155, I need to decrease them by n percent, so they together give 100, but to keep the ratio between them. Not sure is it even possible, any feedback would be great. So a = 5 b = 90 c = 60 How much in percent, I should decrease each number so they give 100, but to keep ration as it is now. Thank you.

First keep in mind that if you decrease each number by the same percentage, their ratio remains same.

$$a \rightarrow a- \frac{na}{100}$$ and $$b \rightarrow b- \frac{nb}{100}$$ $$\implies \frac ab=\frac{a-\frac{na}{100}}{b- \frac{nb}{100}}=\frac ab$$

Now, for your problem, you must have, $$\left(a- \frac{na}{100}\right)+\left(b- \frac{nb}{100}\right)+\left(c- \frac{nc}{100}\right)=100$$ plug in the values of $a,b,c$ and you can find $n$

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