A briefcase with 5 manuals in it has a mass of 1.63 kg. When 4 more manuals and 10 files are added, the mass becomes 2.334 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
1.63 kg = 1.63 x 1000 = 1630 g
2.334 kg = 2.334 x 1000 = 2334 g

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

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 + 5 M = 1630 --- (1)

1 BC + 9 M + 10 F = 2334 --- (2)

From (1)
1 BC + 15 u = 1630 --- (3)

From (2)
1 BC + 27 u + 10 u = 2334
1 BC + 37 u = 2334 --- (4)

(4) - (3)
37 u - 15 u = 2334 - 1630
22 u = 704 

1 u = 704 ÷ 22 = 32

From (1)
1 BC + 15 u = 1630 

From (3)
Mass of the briefcase
= 1630 - 15 u
= 1630 - (15 x 32)
= 1630 - 480
= 1150 g

1150 g = 1150 ÷ 1000 = 1.15 kg

Answer(s): 1.15 kg