## Task B-2.2.

The price of the mobile phone before the first reduction was 200 €. Since the mobile phone was not sold after its price was first reduced, the seller reduced the price again by the same percentage. If the final price of the mobile phone is $162 €$, what was the price of the mobile phone after the first reduction?
## First Solution.

Let $x \%$ be the desired percentage.

After the first reduction, the price of the mobile phone is $200 - x \% \cdot 200 = 200 - 2x$.

After the second reduction, the price of the mobile phone is:

$200 - 2x - x \% \cdot (200 - 2x) = 200 - 2x - 2x + 0.02x^2 = 0.02x^2 - 4x + 200$.

We know that the final price of the mobile phone is 162 €, so by solving the quadratic equation, we determine the desired percentage.
$0.02x^2 - 4x + 200 = 162$

$0.02x^2 - 4x + 38 = 0 \backslash \cdot 50$

$x^2 - 200x + 1900 = 0$

The solutions obtained are $x_1 = 10$ and $x_2 = 190$.

1 point

Since the price cannot be reduced by more than $100 \%$, we conclude that the price was reduced by $10 \%$ both times.

The price of the mobile phone after the first reduction was $200 - 2 \cdot 10 = 180 €$.

1 point