A briefcase with 4 magazines in it has a mass of 1.964 kg. When 5 more magazines and 8 guide books are added, the mass becomes 2.828 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
1.964 kg = 1.964 x 1000 = 1964 g
2.828 kg = 2.828 x 1000 = 2828 g

Number of magazines in the end
= 4 + 5
= 9

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 = 1964 --- (1)

1 BC + 9 M + 8 G = 2828 --- (2)

From (1)
1 BC + 8 u = 1964 --- (3)

From (2)
1 BC + 18 u + 8 u = 2828
1 BC + 26 u = 2828 --- (4)

(4) - (3)
26 u - 8 u = 2828 - 1964
18 u = 864 

1 u = 864 ÷ 18 = 48

From (1)
1 BC + 8 u = 1964 

From (3)
Mass of the briefcase
= 1964 - 8 u
= 1964 - (8 x 48)
= 1964 - 384
= 1580 g

1580 g = 1580 ÷ 1000 = 1.58 kg

Answer(s): 1.58 kg