5.5. Four dolls and five robots cost 4100 rubles, while five dolls and four robots cost 4000. How much does one doll cost?
Answer: 400 rubles.

Solution. Let's briefly write down the condition of the problem:

$$
\begin{aligned}
& 4 \kappa + 5 p = 4100 \\
& 5 \kappa + 4 p = 4000 .
\end{aligned}
$$

Then $9 \kappa + 9 p = 8100$ and the cost of one doll together with one robot will be 900 rubles. Therefore, 4 dolls and 4 robots cost 3600 rubles, which means one doll costs 400 rubles.