A store held a promotional day on its second anniversary. Customers who spent more than $50000 \mathrm{Ft}$ were eligible for a double discount. The discounts were positive integers less than 10 percent. A $69000 \mathrm{Ft}$ television could be purchased for $60306 \mathrm{Ft}$. What were the percentages of the individual discounts?
I. solution. The price after the two price reductions can be expressed by the following equation, where the magnitude of the price reduction in percent is $0<x ; y<10$ integers:

$$
\begin{gathered}
\left(69000 \cdot \frac{100-x}{100}\right) \frac{100-y}{100}=60306 \\
(100-x)(100-y)=8740 \\
10000-100 y-100 x+x y=8740 \\
1260=100(x+y)-x y
\end{gathered}
$$

Given the condition $0<x ; y<10$, $x y$ cannot be greater than 81, and $100(x+y)$ ends in two zeros, so $100(x+y)=$ 1300, which means $x+y=13$ and $x y=40$. Substituting $x=13-y$ we get:

$$
(13-y) y=40, \quad 0=y^{2}-13 y+40, \quad(y-5)(y-8)=0
$$

Thus, the magnitudes of the discounts are $5 \%$ and $8 \%$.

II. solution. Suppose the price of the television was reduced to $p_{1} \%$ and then to $p_{2} \%$ during the two price reductions. Since the discounts in percent were positive integers less than 10, it follows that $91 \leq p_{1} \leq 99$ and $91 \leq p_{2} \leq 99, p_{1} ; p_{2} \in \mathbb{N}^{+}$

Based on the condition regarding the change in the price of the television: $69000 \frac{p_{1}}{100} \frac{p_{2}}{100}=60306$, from which $p_{1} p_{2}=8740$.

Since 5 | 8740 and 5 is a prime number, it follows that $5 \mid p_{1}$, or $5 \mid p_{2}$. The only positive integer divisible by 5 in the [91;99] interval is 95, so one of $p_{1}$ and $p_{2}$ must be 95, while the other is $\frac{8740}{95}=92,\left(\left\{p_{1} ; p_{2}\right\}=\{92 ; 95\}\right)$.

These also satisfy the conditions of the problem, since

$$
69000 \frac{95}{100} \frac{92}{100}=69000 \frac{92}{100} \frac{95}{100}=60306
$$

If the price of the television changed to 95% and then to 92% (or vice versa) during the two price reductions, then the individual discounts were: $5 \%$ and $8 \%$.