A briefcase with 5 magazines in it has a mass of 2.72 kg. When 3 more magazines and 11 guide books are added, the mass becomes 3.162 kg. Each magazine has a mass 2 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
2.72 kg = 2.72 x 1000 = 2720 g
3.162 kg = 3.162 x 1000 = 3162 g

Number of magazines in the end
= 5 + 3
= 8

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 = 2 u

1 BC + 5 M = 2720 --- (1)

1 BC + 8 M + 11 G = 3162 --- (2)

From (1)
1 BC + 10 u = 2720 --- (3)

From (2)
1 BC + 16 u + 11 u = 3162
1 BC + 27 u = 3162 --- (4)

(4) - (3)
27 u - 10 u = 3162 - 2720
17 u = 442 

1 u = 442 ÷ 17 = 26

From (1)
1 BC + 10 u = 2720 

From (3)
Mass of the briefcase
= 2720 - 10 u
= 2720 - (10 x 26)
= 2720 - 260
= 2460 g

2460 g = 2460 ÷ 1000 = 2.46 kg

Answer(s): 2.46 kg