Problem 1. The watermelon and the cantaloupe have a total mass of $30 \mathrm{~kg}$. The cantaloupe and a 3 $\mathrm{kg}$ weight have half the mass of the watermelon. What is the difference in kilograms between the mass of the watermelon and the cantaloupe?
Solution. Since the mass of one watermelon is twice the mass of one melon plus $3 \mathrm{~kg}$, this means that the mass of one watermelon is equal to the mass of two melons plus $6 \mathrm{~kg}$. The watermelon and the melon together have a mass of $30 \mathrm{~kg}$, so two melons plus one more melon and $6 \mathrm{~kg}$ have a mass of $30 \mathrm{~kg}$, which means three melons and $6 \mathrm{~kg}$ have a mass of $30 \mathrm{~kg}$. Therefore, three melons have a mass of $30-6=24 \mathrm{~kg}$, so one melon has a mass of $24: 3=8 \mathrm{~kg}$. According to this, the mass of the watermelon is $30-8=22 \mathrm{~kg}$, so the difference in mass between the watermelon and the melon is $22-8=14 \mathrm{~kg}$.