How to calculate X with: percent of X = Y

Question

I am sorry if this is impossible to compute in one equatation.

I am trying to compute the following:
for example

y = 574  
x - ((16% of x) + y) = 0

the goal is to find out what is x so as to make it equal to 0.

I have managed to reach the number but only using a loop in a programming function, lets say x starts at 1111, so in that loop i did -1 until it reached the desired 0.

I was wondering how to organize the equatation to find out x in one go.

basically, is it possible to find out x here:

0 = x - ((16% of x) + 574)

if so, please advice how?

I tried to search in google but I had no clue how this kind of math is defined.

Thank you

edit of what I tried so far:

I already know by my other calculations that:

 x = 683

for example:

0 = x - ((16% of x) + 574)
0 = 683 - ((109.28) + 574 )
0 = 683 - 683.28

but I calculated this programmatically, the question is how to reach this using an equitation.

Answer 1

Given a value of $y$, you want to solve the following for $x$: $$x - (0.16x + y) = 0$$ But that's easy: $$x - (0.16x + y) = 0$$ $$x - 0.16x - y = 0$$ $$(1 - 0.16)x - y= 0$$ $$0.84 x-y = 0$$ $$0.84 x = y$$ $$x = \dfrac{y}{0.84}$$ In the specific case $y=574$: $$x = \dfrac{574}{0.84}\approx 683.3333$$ Check: $$x - (0.16x + y) = 683.3333 - (0.16(683.3333) + 574) \approx 0$$ The result is only approximately zero here (and not exactly zero) because we rounded the value for $x$. The actual value is $683\frac13$, which has an infinitely repeating decimal representation $683.\bar{3}$ .