A briefcase with 4 manuals in it has a mass of 1.374 kg. When 5 more manuals and 8 files are added, the mass becomes 1.878 kg. Each manual has a mass 2 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
1.374 kg = 1.374 x 1000 = 1374 g
1.878 kg = 1.878 x 1000 = 1878 g

Number of manuals in the end
= 4 + 5
= 9

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 = 2 u

1 BC + 4 M = 1374 --- (1)

1 BC + 9 M + 8 F = 1878 --- (2)

From (1)
1 BC + 8 u = 1374 --- (3)

From (2)
1 BC + 18 u + 8 u = 1878
1 BC + 26 u = 1878 --- (4)

(4) - (3)
26 u - 8 u = 1878 - 1374
18 u = 504 

1 u = 504 ÷ 18 = 28

From (1)
1 BC + 8 u = 1374 

From (3)
Mass of the briefcase
= 1374 - 8 u
= 1374 - (8 x 28)
= 1374 - 224
= 1150 g

1150 g = 1150 ÷ 1000 = 1.15 kg

Answer(s): 1.15 kg