A briefcase with 2 books in it has a mass of 1.456 kg. When 5 more books and 12 files are added, the mass becomes 1.984 kg. Each book 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
1.456 kg = 1.456 x 1000 = 1456 g
1.984 kg = 1.984 x 1000 = 1984 g

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

Let 1 briefcase be 1 BC.
Let 1 book be 1 B.
Let 1 file be 1 F.

Change the books and the files into units.

1 F = 1 u
1 B = 2 u

1 BC + 2 B = 1456 --- (1)

1 BC + 7 B + 12 F = 1984 --- (2)

From (1)
1 BC + 4 u = 1456 --- (3)

From (2)
1 BC + 14 u + 12 u = 1984
1 BC + 26 u = 1984 --- (4)

(4) - (3)
26 u - 4 u = 1984 - 1456
22 u = 528 

1 u = 528 ÷ 22 = 24

From (1)
1 BC + 4 u = 1456 

From (3)
Mass of the briefcase
= 1456 - 4 u
= 1456 - (4 x 24)
= 1456 - 96
= 1360 g

1360 g = 1360 ÷ 1000 = 1.36 kg

Answer(s): 1.36 kg