A store was selling each unit of a toy for $R \$ 13.00$. To sell its entire stock, which was not more than 100 units, the store management decided to lower the price by an integer number of reais, thus obtaining $\mathrm{R} \$ 781.00$ for the entire stock. What was the price reduction, per unit?
If $x$ denotes the discount in reais and $y$ the total number of pieces, then $(13-x) \times y=781$. Thus, $(13-x)$ and $y$ are divisors of 781, and since $781=11 \times 71$, the only divisors of 781 are $1, 11, 71$, and 781. The divisor $13-x$ of 781 cannot be equal to 1, as we know that $y \leq 100$. The only option, then, is $13-x=11$ and $y=71$, so the reduction was $x=\mathrm{R} \$ 2.00$ per unit.