Hi I have a rather basic arithmetic question about percentages which is confusing me:

Let's say you have a variable x that is composed of x1, x2, x3.

You know what (x1 + x2) is, and you also calculated from some other data that x3 is y% of x. How do you now adjust (x1+x2) to get x?

So for example:

(x1+x2)= 55

Y%= .31

Which of the following two is the correct answer for x?

55*(1+.31) OR 55/(1-.31)

The first one you're adding 31% to the 55, but in the second one you assume that the 55 is 69% of x, and so to get 100% you divide 55/.69.

Which is the right one?

• The second one is correct. $\dfrac{55}{0.69}$ Commented Sep 29, 2017 at 8:33
• Thanks much! When is the first answer ever correct? Commented Sep 29, 2017 at 8:42

By

$x_3$ is $y\%$ of $x$

I assume you mean that $x_3$ is $y\%$ of the sum of $x$ (i.e., $x=x_1+x_2+x_3$).

In that case, you know that $x_1+x_2$ is $(1-y)\%$ of the total sum (in your example, that would be $0.69$.

So you have $55=0.69\cdot x$ or $$x=\frac{55}{0.69}$$

• Thank you for the detailed answer! Commented Sep 29, 2017 at 8:40
• How come yours was voted down? Commented Sep 29, 2017 at 8:41
• @sqlfiddler No idea why it was downvoted. The downvoter has the right to do it, although the usual way is to tell the poster why you think the answer deserves a downvote. I'll live, though.
– 5xum
Commented Sep 29, 2017 at 8:45
• I have a follow up question: say you have a ratio of x/y, and you know the value of y, and you now want to increase y by x/y, would you in this case do the following y*(1+(x/y))? Commented Sep 29, 2017 at 8:49
• Pressed enter before giving example: Commented Sep 29, 2017 at 8:50