Arithmetic question about percentages

Question

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?

Answer 1

By

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

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

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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 $$x=\frac{55}{0.69}$$