Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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!

share|cite|improve this question
up vote 1 down vote accepted

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 $z$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.