2. Goran brought $525 \mathrm{~kg}$ of mushrooms to the market. He sold $\frac{3}{5}$ of the total amount of mushrooms at a price of $3 € / \mathrm{kg}$, $\frac{4}{5}$ of the remainder at a price of $5 € / \mathrm{kg}$, and a third of the new remainder at a price of $6 € / \mathrm{kg}$. For how many euros per kilogram did Goran sell the remaining mushrooms if he received a total of $2023 €$?
2. Goran brought $525 \mathrm{~kg}$ of mushrooms to the market. He sold $\frac{3}{5}$ of the total amount of mushrooms at a price of $3 € / \mathrm{kg}$, $\frac{4}{5}$ of the remainder at a price of $5 € / \mathrm{kg}$, and a third of the new remainder at a price of $6 € / \mathrm{kg}$. For how many euros per kilogram did Goran sell the remaining mushrooms if he received a total of $2023 €$?

## Solution.

$\frac{3}{5}$ of $525 \mathrm{~kg}$ is $315 \mathrm{~kg}$. The remainder is $525 \mathrm{~kg}-315 \mathrm{~kg}=210 \mathrm{~kg}$.

$1 \mathrm{POINT}$

$\frac{4}{5}$ of $210 \mathrm{~kg}$ is $168 \mathrm{~kg}$. The remainder is $210 \mathrm{~kg}-168 \mathrm{~kg}=42 \mathrm{~kg}$.

$1 \mathrm{POINT}$

A third of 42 is $42: 3=14 \mathrm{~kg}$. The remainder is $42 \mathrm{~kg}-14 \mathrm{~kg}=28 \mathrm{~kg}$.

$1 \mathrm{POINT}$

(Note: The following process can also be scored 3 POINTS:

If he sold $\frac{3}{5}$ of the total amount of mushrooms, $\frac{2}{5}$ of the total amount of mushrooms remained, i.e., $\frac{2}{5}$ of $525 \mathrm{~kg}$, which is $210 \mathrm{~kg}$.

If he sold $\frac{4}{5}$ of the remainder, then $\frac{1}{5}$ of the remainder of mushrooms remained, i.e., $\frac{1}{5}$ of $210 \mathrm{~kg}$, which is $42 \mathrm{~kg}$.

If he sold a third of the new remainder, then $\frac{2}{3}$ of the new remainder remained, i.e., $\frac{2}{3}$ of $42 \mathrm{~kg}$, which is $28 \mathrm{~kg}$.)

Let $x$ be the price at which he sold the remaining $28 \mathrm{~kg}$ of mushrooms.

We have:

$315 \cdot 3+168 \cdot 5+14 \cdot 6+28 x=2023 \quad 1 \mathrm{POINT}$

$945+840+84+28 x=2023$

$1869+28 x=2023$

$1 \mathrm{POINT}$

$28 x=2023-1869$

$28 x=154$

$x=154: 28$

$x=5.5$

The remaining mushrooms should be sold for $5.50 € / \mathrm{kg}$.

$1 \mathrm{POINT}$

TOTAL 6 POINTS