Three customers are at the hairdresser's, each paying their bill at the cash register.

- the first customer pays the same amount that is in the cash register and takes out 10 reais as change;
- the second customer performs the same operation as the first;
- the third customer performs the same operation as the first two.

Find the initial amount that was in the cash register, knowing that at the end of the three operations the cash register is empty.
Let $x$ be the initial amount in the cash register. This amount plus what the 3 customers paid will result in a zero balance.

- The 1st customer pays $x-10$. After the first customer, there are $x+x-10=2 x-10$ reais in the cash register.
- The 2nd customer pays $(2 x-10)-10=2 x-20$. After the 20th customer, there are $(2 x-10)+(2 x-20)=4 x-30$ in the cash register.
- The 3rd customer pays $(4 x-30)-10=4 x-40$. After the 30th customer, there are $(4 x-30)+(4 x-40)=8 x-70$ in the cash register, which we know is equal to 0.

Therefore, $8 x=70$ and we get $x=8.75$ reais.