find the number b where a = b + 19% of b

Question

Find which number plus its 19% gives for example 200, 233 ..

Story short: for example I have the number 0.30 now I need to know with formula how can I get which number plus its 19% gives 0.30 ?

I know this must be simple math but I am not so good with it.

Answer 1

You want $n=1.19m$, so $m=\frac n{1.19}$ For $n=0.30, m \approx 0.2521$

Answer 2

We'll let $a$ represent the "end" amount, in decimal (so $a = 0.30$ corresponds with an end amount at $30\%$ e.g.), and we'll let $b$ represents the "starting quantity" we are interested in finding (the amount we started with before adding $19\%$ to it, to get $a$). Then

$$a = b + 0.19 b = 1.19 b \iff b = \frac{a}{1.19}$$

So if we want to know what number $b$ plus $19\%$ gives $a = 2.33$ ($233\%$), then we compute

$$b = \frac{2.33}{1.19} \approx 1.9580, \;\text{ or} \;\;195.80\%$$