A bottle has a mass of 1.8 kilograms when it is completely filled with juice. It has a mass of 1.23?

WANTED: The mass of a bottle in kg (kilogram).
GIVEN:
The mass of the bottle plus that of 1/1 [1/1 = 8/8] of the bottle's not otherwise specified volume of juice (1.8kg).
The mass of the bottle plus that of 5/8 [1/1 - 3/8] of the bottle's not otherwise specified volume of juice (1.23kg).

We calculate only masses. All masses are in kg (kilograms). So, I won't write down the unit in the calculation.

mass empty bottle := b
mass juice := j

8/8 j + b = 1.8
5/8 j + b = 1.23

The difference is:

3/8 j = 0.57

Dividing that by 3 gives you the mass of 1/8-th of the juice. That times 8 yields the mass of the juice when the bottle is flled. So, we combine that:

1 j = (0.57 / (3/8)) = ((0.57 * 8) / 3) = 1.52

1.52 + b = 1.8
b = 1.8 - 1.52 = 0.82

Solution:
The empty bottle has a mass of 0.82kg or 280g.