A briefcase with 5 books in it has a mass of 1.85 kg. When 3 more books and 8 files are added, the mass becomes 2.382 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
1.85 kg = 1.85 x 1000 = 1850 g
2.382 kg = 2.382 x 1000 = 2382 g

Number of books in the end
= 5 + 3
= 8

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 + 5 B = 1850 --- (1)

1 BC + 8 B + 8 F = 2382 --- (2)

From (1)
1 BC + 10 u = 1850 --- (3)

From (2)
1 BC + 16 u + 8 u = 2382
1 BC + 24 u = 2382 --- (4)

(4) - (3)
24 u - 10 u = 2382 - 1850
14 u = 532 

1 u = 532 ÷ 14 = 38

From (1)
1 BC + 10 u = 1850 

From (3)
Mass of the briefcase
= 1850 - 10 u
= 1850 - (10 x 38)
= 1850 - 380
= 1470 g

1470 g = 1470 ÷ 1000 = 1.47 kg

Answer(s): 1.47 kg