Task B-1.4. A trader has decided to purchase dried plums for further sale. For half of his currently available money, he bought plums from a producer whose price was $30 \mathrm{kn}$ per kilogram. With the other half of the money, he went to another producer and managed to buy half the quantity of plums more than from the first one. He mixed the plums. At what price per kilogram should the trader now sell the plums to earn $5 \mathrm{kn}$ per kilogram sold?
## Solution.

Let's introduce the following notations.

$x$ - the quantity of plums bought from the 1st producer (in kilograms)

$x+\frac{1}{2} x-$ the quantity of plums bought from the 2nd producer (in kilograms)
$c_{2}$ - the price from the second producer

$c$ - the price of the mixture.

Then $x \cdot 30=\left(x+\frac{1}{2} x\right) \cdot c_{2}$,

or $c_{2}=20 \text{ kn}$.

The price of the mixture is calculated from the following equality.

$x \cdot 30+\left(x+\frac{1}{2} x\right) \cdot 20=\left(x+x+\frac{1}{2} x\right) \cdot c$.

After simplification, we get

$120 x=5 x c$.

It follows that $c=24 \text{ kn}$.

(1 point)

To make a profit of $5 \text{ kn}$ per kilogram sold, the trader must sell the plums at $24+5=29$ kn per kilogram.