A briefcase with 4 magazines in it has a mass of 2.454 kg. When 2 more magazines and 3 guide books are added, the mass becomes 2.79 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
2.454 kg = 2.454 x 1000 = 2454 g
2.79 kg = 2.79 x 1000 = 2790 g

Number of magazines in the end
= 4 + 2
= 6

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 + 4 M = 2454 --- (1)

1 BC + 6 M + 3 G = 2790 --- (2)

From (1)
1 BC + 8 u = 2454 --- (3)

From (2)
1 BC + 12 u + 3 u = 2790
1 BC + 15 u = 2790 --- (4)

(4) - (3)
15 u - 8 u = 2790 - 2454
7 u = 336 

1 u = 336 ÷ 7 = 48

From (1)
1 BC + 8 u = 2454 

From (3)
Mass of the briefcase
= 2454 - 8 u
= 2454 - (8 x 48)
= 2454 - 384
= 2070 g

2070 g = 2070 ÷ 1000 = 2.07 kg

Answer(s): 2.07 kg