A briefcase with 3 manuals in it has a mass of 2.356 kg. When 5 more manuals and 12 files are added, the mass becomes 3.004 kg. Each manual has a mass 3 times as much as each file. Find the mass of the briefcase when it is empty. Express the answer in kg.
1 kg = 1000 g
2.356 kg = 2.356 x 1000 = 2356 g
3.004 kg = 3.004 x 1000 = 3004 g

Number of manuals in the end
= 3 + 5
= 8

Let 1 briefcase be 1 BC.
Let 1 manual be 1 M.
Let 1 file be 1 F.

Change the manuals and the files into units.

1 F = 1 u
1 M = 3 u

1 BC + 3 M = 2356 --- (1)

1 BC + 8 M + 12 F = 3004 --- (2)

From (1)
1 BC + 9 u = 2356 --- (3)

From (2)
1 BC + 24 u + 12 u = 3004
1 BC + 36 u = 3004 --- (4)

(4) - (3)
36 u - 9 u = 3004 - 2356
27 u = 648 

1 u = 648 ÷ 27 = 24

From (1)
1 BC + 9 u = 2356 

From (3)
Mass of the briefcase
= 2356 - 9 u
= 2356 - (9 x 24)
= 2356 - 216
= 2140 g

2140 g = 2140 ÷ 1000 = 2.14 kg

Answer(s): 2.14 kg