A $21250 \mathrm{Ft}$ coat was discounted during a generous sale. Then, during the Christmas market, it became even cheaper at a promotional price of $19176 \mathrm{Ft}$. What are the percentages of the discounts, given that both are single-digit numbers?
The price of the coat was first reduced by $p \%$, and then by $q \%$, so the final price is

$$
21250\left(1-\frac{p}{100}\right)\left(1-\frac{q}{100}\right)=19176
$$

After performing the multiplications and rearranging the equation, we get

$$
100^{2}-100 p-100 q-p q=9024
$$

From this,

$$
p \cdot q+976=100(p+q)
$$

We know that $p$ and $q$ are single-digit numbers, so $p \cdot q \leq 81$. The right side is divisible by 100, so $900<p q+976 \leq 1057$ must also be divisible by 100, which is only possible if $p q+976=1000$. From this, $p q=24$, and from (1) $p+q=10$, from which $p=4$ and $q=6$ (or vice versa).

Indeed, 6% of 21250 is 1275, so the price of the coat after the first reduction was 19975 Ft, and reducing this by 4% - 799 - we get that the price of the coat after the price reductions is $19176 \mathrm{Ft}$.

Bertalan Németh (Kecskemét, Bányai Júlia Gymnasium, 9th grade)