1. In a full container, there are 150 watermelons and melons for a total of 24 thousand rubles, with all the watermelons together costing as much as all the melons. How much does one watermelon cost, given that the container can hold 120 melons (without watermelons) and 160 watermelons (without melons)?
Answer: 100 rubles. Solution. Let there be $x$ watermelons, then there will be $150-x$ melons. If a container can hold 120 melons, then one melon occupies $\frac{1}{120}$ of the container. Similarly, one watermelon occupies $\frac{1}{160}$ of the container. Therefore, if the container is fully loaded with 150 watermelons and melons (and the container is full), then $\frac{x}{160}+\frac{150-x}{120}=1$. From this, $x=120$. So, there were 120 watermelons and 30 melons. If a watermelon costs $a$ rubles, and a melon costs $b$ rubles, then (since the cost of watermelons and melons is the same): $120 a=30 b=12000$. Therefore, $a=100, b=400$.