I 'reverse engineered' a problem about percents but need help understanding it.

Question

Tapiwa raked 5% more leaves than Adam raked. Tapiwa raked 357 liters of leaves

How many liters of leaves did Adam rake?

It is a question on one of my homework problems about percentages. I had no idea where to start from so I began by getting 5% of 357 which is 17.85, I then subtracted it from 357 and got 341.15; I thought maybe that was the answer so I tested it to see if it as true.

341.15 $\bullet$ 0.05 = 17.0575

341.15 + 17.0575 = 358.2075

Well 341.15 isn't the answer so after that I decided to play around with it and I found out that 340 is the correct answer

340 $\bullet$ 0.05 = 17

340 + 17 = 357

Adam raked 340 liters of leaves.

Since I found the answer I though I could work back and figure out some 'equation' or 'formula' (that I should have used at first) however, I couldn't so I find myself here asking you guys, the masters for help.

What should have I done?

Answer 1

Let $x$ the raked of Adam. So, I have:$$x+\frac{1}{20}x=357$$From this I obtain $x=340$.

Answer 2

Let $t$ be the number of Tapiwa leaves and $a$ the one of Adam.

Then $t=105\%\cdot a$. But as $t=357$ we get $a=\frac{357}{105\%}=\frac{357}{1.05}$