A briefcase with 5 books in it has a mass of 1.5 kg. When 3 more books and 11 files are added, the mass becomes 1.94 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
1.5 kg = 1.5 x 1000 = 1500 g
1.94 kg = 1.94 x 1000 = 1940 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 = 3 u

1 BC + 5 B = 1500 --- (1)

1 BC + 8 B + 11 F = 1940 --- (2)

From (1)
1 BC + 15 u = 1500 --- (3)

From (2)
1 BC + 24 u + 11 u = 1940
1 BC + 35 u = 1940 --- (4)

(4) - (3)
35 u - 15 u = 1940 - 1500
20 u = 440 

1 u = 440 ÷ 20 = 22

From (1)
1 BC + 15 u = 1500 

From (3)
Mass of the briefcase
= 1500 - 15 u
= 1500 - (15 x 22)
= 1500 - 330
= 1170 g

1170 g = 1170 ÷ 1000 = 1.17 kg

Answer(s): 1.17 kg