A briefcase with 2 manuals in it has a mass of 1.828 kg. When 5 more manuals and 6 files are added, the mass becomes 2.34 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
1.828 kg = 1.828 x 1000 = 1828 g
2.34 kg = 2.34 x 1000 = 2340 g

Number of manuals in the end
= 2 + 5
= 7

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 + 2 M = 1828 --- (1)

1 BC + 7 M + 6 F = 2340 --- (2)

From (1)
1 BC + 4 u = 1828 --- (3)

From (2)
1 BC + 14 u + 6 u = 2340
1 BC + 20 u = 2340 --- (4)

(4) - (3)
20 u - 4 u = 2340 - 1828
16 u = 512 

1 u = 512 ÷ 16 = 32

From (1)
1 BC + 4 u = 1828 

From (3)
Mass of the briefcase
= 1828 - 4 u
= 1828 - (4 x 32)
= 1828 - 128
= 1700 g

1700 g = 1700 ÷ 1000 = 1.7 kg

Answer(s): 1.7 kg