A briefcase with 3 manuals in it has a mass of 1.79 kg. When 2 more manuals and 12 files are added, the mass becomes 2.33 kg. Each manual 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
1.79 kg = 1.79 x 1000 = 1790 g
2.33 kg = 2.33 x 1000 = 2330 g

Number of manuals in the end
= 3 + 2
= 5

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 = 3 u

1 BC + 3 M = 1790 --- (1)

1 BC + 5 M + 12 F = 2330 --- (2)

From (1)
1 BC + 9 u = 1790 --- (3)

From (2)
1 BC + 15 u + 12 u = 2330
1 BC + 27 u = 2330 --- (4)

(4) - (3)
27 u - 9 u = 2330 - 1790
18 u = 540 

1 u = 540 ÷ 18 = 30

From (1)
1 BC + 9 u = 1790 

From (3)
Mass of the briefcase
= 1790 - 9 u
= 1790 - (9 x 30)
= 1790 - 270
= 1520 g

1520 g = 1520 ÷ 1000 = 1.52 kg

Answer(s): 1.52 kg