1. A certain man hired a worker for a year, promising to give him 12 rubles and a coat. But by chance, after working for 7 months, the worker wanted to leave and asked for a fair payment including the coat. He was given 5 rubles and the coat as fair compensation. What was the value of the coat? (An old problem) Give the answer in rubles, rounding to the nearest hundredth if necessary.

$\{4,8\}$
Solution. This is problem E. D. Voityakhovsky from "A Course in Pure Mathematics" (1811). If the annual fee is $12+K$ (where $K$ is the cost of the caftan), then for 7 months, the payment should be $\frac{7(12+K)}{12}$. We get the equation $\frac{7(12+K)}{12}=5+K$, from which $\frac{5 K}{12}=2, K=\frac{24}{5}=4.8$ rubles. Answer: 4.8.