A briefcase with 5 manuals in it has a mass of 2.29 kg. When 6 more manuals and 4 files are added, the mass becomes 2.642 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
2.29 kg = 2.29 x 1000 = 2290 g
2.642 kg = 2.642 x 1000 = 2642 g

Number of manuals in the end
= 5 + 6
= 11

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 + 5 M = 2290 --- (1)

1 BC + 11 M + 4 F = 2642 --- (2)

From (1)
1 BC + 10 u = 2290 --- (3)

From (2)
1 BC + 22 u + 4 u = 2642
1 BC + 26 u = 2642 --- (4)

(4) - (3)
26 u - 10 u = 2642 - 2290
16 u = 352 

1 u = 352 ÷ 16 = 22

From (1)
1 BC + 10 u = 2290 

From (3)
Mass of the briefcase
= 2290 - 10 u
= 2290 - (10 x 22)
= 2290 - 220
= 2070 g

2070 g = 2070 ÷ 1000 = 2.07 kg

Answer(s): 2.07 kg