# How to compute effect of change in 1 item's percentage on the others, while maintaining 100%?

Consider three variables x, y, z = 20%, 30%, 50% respectively. Now, let's say i bump up x to 50%. I want to compute the new percentages of y and z to maintain the 100% while in the original ratio of 2:3:5.

I've come up with a non-elegant, messy solution here which i'm not sure is even right and i'm hoping i can construct something more simple and elegant:

1. Get ratio of y and z w.r.t x that is = 3/2 and 5/2 respectively
2. Find out the difference between 100% and the new value of x = 100 - 50 = 50
3. Create an equation as such (3/2)m + (5/2)m = 50 and solve for m. hence, m = 12.5
4. y = 12.5 * (3/2) = 18.75
5. z = 12.5 * (5/2) = 31.25

I'm sure i'm being stupid and missing out on a very basic ratio equation here. Please help me remember. Thanks!

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I believe you mean that you want to maintain the original $3:5$ ratio between $y$ and $z$.
Since $x$ has grown to $50\%$, the new $y$ and $z$ must add up to $50\%$. So $y$ must be $\frac{3}{8}$ of that, and $z$ must be $\frac{5}{8}$ of that.
Thus, as a percentage, $y$ is now $\frac{150}{8}=18.75$. quite This is essentially what you did, perhaps done a little more efficiently. The logic of your calculation is quite clear, you had the problem under control.
If your $x$ has changed to say $40\%$ instead of $50\%$, we multiply $60$ by $\frac{3}{8}$ and $\frac{5}{8}$ respectively to calculate the new $y$ and $z$.