A briefcase with 3 books in it has a mass of 2.056 kg. When 4 more books and 11 files are added, the mass becomes 2.838 kg. Each book has a mass 3 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
2.056 kg = 2.056 x 1000 = 2056 g
2.838 kg = 2.838 x 1000 = 2838 g

Number of books in the end
= 3 + 4
= 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 = 3 u

1 BC + 3 B = 2056 --- (1)

1 BC + 7 B + 11 F = 2838 --- (2)

From (1)
1 BC + 9 u = 2056 --- (3)

From (2)
1 BC + 21 u + 11 u = 2838
1 BC + 32 u = 2838 --- (4)

(4) - (3)
32 u - 9 u = 2838 - 2056
23 u = 782 

1 u = 782 ÷ 23 = 34

From (1)
1 BC + 9 u = 2056 

From (3)
Mass of the briefcase
= 2056 - 9 u
= 2056 - (9 x 34)
= 2056 - 306
= 1750 g

1750 g = 1750 ÷ 1000 = 1.75 kg

Answer(s): 1.75 kg