Arithmetic question about percentages 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?
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 $$x=\frac{55}{0.69}$$
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 $$x=\frac{55}{0.69}$$