A store received a shipment of walnuts and peanuts in $1 \mathrm{~kg}$ packages. The invoice only stated that the value of the shipment was $1978 \mathrm{Ft}$, and its weight was $55 \mathrm{~kg}$. The delivery people remembered the following:
- the walnuts were more expensive;

- the price per kilogram is a two-digit number, and one can be obtained from the other by swapping the digits;
- the price of walnuts consists of adjacent digits. How much does $1 \mathrm{~kg}$ of walnuts cost?
If the price of walnuts and peanuts were equal, they would cost $1978: 55=35.9 \ldots$ Ft. Therefore, according to the first condition, the walnut had to cost more than 35.9 Ft, and the peanut less than that. Such a pair of numbers that also satisfies the second and third conditions is only one, which is 43, 34. Therefore, the walnut could only cost $43 \mathrm{Ft}$, and the peanut $34 \mathrm{Ft}$. Based on this, setting up the equation $34(55-d)+43 d=1978$ for the value of the shipment - where $d$ represents the quantity of walnuts - and solving it, we get that $d=12$, meaning that with these prices, all other conditions are also satisfied: $12 \mathrm{~kg}$ of walnuts and $43 \mathrm{~kg}$ of peanuts were brought. Therefore, the kilogram of walnuts cost $43 \mathrm{Ft}$.