A briefcase with 4 files in it has a mass of 1.284 kg. When 5 more files and 9 magazines are added, the mass becomes 1.816 kg. Each file has a mass 2 times as much as each magazine. Find the mass of the briefcase when it is empty. Express the answer in kg.
1 kg = 1000 g
1.284 kg = 1.284 x 1000 = 1284 g
1.816 kg = 1.816 x 1000 = 1816 g

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

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

Change the files and the magazines into units.

1 M = 1 u
1 F = 2 u

1 BC + 4 F = 1284 --- (1)

1 BC + 9 F + 9 M = 1816 --- (2)

From (1)
1 BC + 8 u = 1284 --- (3)

From (2)
1 BC + 18 u + 9 u = 1816
1 BC + 27 u = 1816 --- (4)

(4) - (3)
27 u - 8 u = 1816 - 1284
19 u = 532 

1 u = 532 ÷ 19 = 28

From (1)
1 BC + 8 u = 1284 

From (3)
Mass of the briefcase
= 1284 - 8 u
= 1284 - (8 x 28)
= 1284 - 224
= 1060 g

1060 g = 1060 ÷ 1000 = 1.06 kg

Answer(s): 1.06 kg