Problem 5.2. On the table lie an orange, a banana, a tangerine, a peach, and an apple. Their weights are 100 g, 150 g, 170 g, 200 g, 280 g, but it is unknown which fruit weighs how much.

It is known that:

- the peach is lighter than the orange
- the banana is heavier than the apple, but lighter than the peach
- the tangerine is lighter than the banana
- the apple and the banana together are heavier than the orange.

How much does each fruit weigh?
Answer: Mandarin - 100 g, apple - 150 g, banana - 170 g, peach - 200 g, orange 280 g.

Solution. From the first two statements, it follows that the apple is lighter than the banana, the banana is lighter than the peach, the peach is lighter than the orange. From the third statement, it follows that the mandarin is also lighter than the banana. This can be schematically written as: a, m < b < p < a.

We know that the apple and the mandarin are the lightest fruits, but we don't yet know which one is lighter. For the other fruits, we know that they are heavier and we know how they are ordered by weight. It turns out that the orange weighs 280 g, the peach - 200 g, the banana - 170 g.

It remains to establish the correspondence between the masses of 100 g, 150 g, and the apple, mandarin. If the apple weighs 100 g, then together with the banana, they weigh 270 g, which is less than 280 g, so the last condition is not met. Therefore, the mandarin weighs 100 g, and the apple - 150 g.