A briefcase with 2 magazines in it has a mass of 1.224 kg. When 3 more magazines and 10 guide books are added, the mass becomes 1.68 kg. Each magazine has a mass 3 times as much as each guide book. Find the mass of the briefcase when it is empty. Express the answer in kg.
1 kg = 1000 g
1.224 kg = 1.224 x 1000 = 1224 g
1.68 kg = 1.68 x 1000 = 1680 g

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

Let 1 briefcase be 1 BC.
Let 1 magazine be 1 M.
Let 1 guide book be 1 G.

Change the magazines and the guide books into units.

1 G = 1 u
1 M = 3 u

1 BC + 2 M = 1224 --- (1)

1 BC + 5 M + 10 G = 1680 --- (2)

From (1)
1 BC + 6 u = 1224 --- (3)

From (2)
1 BC + 15 u + 10 u = 1680
1 BC + 25 u = 1680 --- (4)

(4) - (3)
25 u - 6 u = 1680 - 1224
19 u = 456 

1 u = 456 ÷ 19 = 24

From (1)
1 BC + 6 u = 1224 

From (3)
Mass of the briefcase
= 1224 - 6 u
= 1224 - (6 x 24)
= 1224 - 144
= 1080 g

1080 g = 1080 ÷ 1000 = 1.08 kg

Answer(s): 1.08 kg