Mrs. Kucera was on a seven-day vacation, and Káta walked her dog and fed her rabbits for the entire duration. For this, she received a large cake and 700 CZK. After another vacation, this time a four-day one, Káta received the same cake and 340 CZK for walking and feeding according to the same rules.

What was the value of the cake?
If $d$ is the unknown price of the cake, then $d+700$ Kč is the seven-day reward for Káta. The reward for one day is $\frac{1}{7} d+100$ Kč, for four days it should be $\frac{4}{7} d+400$ Kč. However, the reward was $d+340$ Kč, which is $\frac{3}{7} d$ more and 60 Kč less. Thus, $\frac{3}{7}$ of the cake corresponds to 60 Kč, $\frac{1}{7}$ of the cake is 20 Kč, and the whole cake is $7 \cdot 20=140$ (Kč).

Another solution. Káta worked 3 days less the second time and received $700-340=360$ (Kč) less (the cake had the same price). This means that she earned $360: 3=120$ (Kč) per day. For four days of work, she earned $4 \cdot 120=480$ (Kč), but she received one cake and 340 Kč. The price of the cake is therefore $480-340=140$ (Kč).

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