13.433 Enterprise $A$, which consumes ice, purchases it at point $B$ at a price of $a$ rubles per ton. Sometimes this enterprise has to buy ice from another point $C$ at a price of 1.5 $a$ rubles per ton. Both manufacturers deliver the purchased ice to consumer $A$ themselves, charging $p$ rubles per ton-kilometer for transportation. The loss in mass due to melting during transportation is $n / 1000$ of the mass per kilometer of the route. Enterprise $A$ is located between $B$ and $C$, and each ton of actually received ice costs the enterprise $A$ the same amount (in rubles) whether delivered from point $B$ or point $C$. How much does one ton of received ice cost enterprise $A$ if it is known that the distance from $B$ to $C$ via $A$ is $s$ km?
Solution. Let $x$ and $y$ be the distances between $B$ and $A$ and between $C$ and $A$ respectively, and $z$ be the actual (real) price of 1 ton of ice. Then, in $A$, $\left(1 \frac{x n}{1000}\right)$ fraction of each ton of ice sent from $B$ and $\left(1 \frac{y n}{1000}\right)$ fraction of each ton of ice sent from $C$ is delivered. According to the condition,

$$
\left\{\begin{array}{l}
z\left(1-\frac{x n}{1000}\right)=a+p x, \\
z\left(1-\frac{y n}{1000}\right)=1.5 a+p y
\end{array} \Rightarrow z\left(2-\frac{n}{1000}(x+y)\right)=2.5 a+p(x+y) \Leftrightarrow\right.
$$

From here, we find $z$.

Answer: $\frac{(2.5 a+p s) 1000}{2000-n s}$ rubles.