A briefcase with 4 books in it has a mass of 1.65 kg. When 6 more books and 3 magazines are added, the mass becomes 2.49 kg. Each book has a mass 3 times as much as each magazine. Find the mass of the briefcase when it is empty. Express the answer in kg.
1 kg = 1000 g
1.65 kg = 1.65 x 1000 = 1650 g
2.49 kg = 2.49 x 1000 = 2490 g

Number of books in the end
= 4 + 6
= 10

Let 1 briefcase be 1 BC.
Let 1 book be 1 B.
Let 1 magazine be 1 M.

Change the books and the magazines into units.

1 M = 1 u
1 B = 3 u

1 BC + 4 B = 1650 --- (1)

1 BC + 10 B + 3 M = 2490 --- (2)

From (1)
1 BC + 12 u = 1650 --- (3)

From (2)
1 BC + 30 u + 3 u = 2490
1 BC + 33 u = 2490 --- (4)

(4) - (3)
33 u - 12 u = 2490 - 1650
21 u = 840 

1 u = 840 ÷ 21 = 40

From (1)
1 BC + 12 u = 1650 

From (3)
Mass of the briefcase
= 1650 - 12 u
= 1650 - (12 x 40)
= 1650 - 480
= 1170 g

1170 g = 1170 ÷ 1000 = 1.17 kg

Answer(s): 1.17 kg