A full vessel with water weighs 5 kg and a half-filled vessel weighs 3 kg how much does an empty vessel weigh.

Let us denote the weight of an empty vessel as x, and the weight of water in a completely filled vessel as y.

From the condition of the problem it is known that a fully filled vessel with water weighs 5 kg, and the weight of a vessel filled up to half is 3 kg, therefore, we can write the following ratios:

x + y = 5;

x + y / 2 = 3.

Substituting into the second equation the value y = 5 – x from the first equation, we get:

x + (5 – x) / 2 = 3;

2 * (x + (5 – x) / 2) = 2 * 3;

2x + 5 – x = 6;

x + 5 = 6;

x = 6 – 5;

x = 1 kg.

Answer: An empty vessel weighs 1 kg.