A briefcase with 5 magazines in it has a mass of 1.64 kg. When 2 more magazines and 6 guide books are added, the mass becomes 2.144 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
1.64 kg = 1.64 x 1000 = 1640 g
2.144 kg = 2.144 x 1000 = 2144 g

Number of magazines in the end
= 5 + 2
= 7

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 + 5 M = 1640 --- (1)

1 BC + 7 M + 6 G = 2144 --- (2)

From (1)
1 BC + 15 u = 1640 --- (3)

From (2)
1 BC + 21 u + 6 u = 2144
1 BC + 27 u = 2144 --- (4)

(4) - (3)
27 u - 15 u = 2144 - 1640
12 u = 504 

1 u = 504 ÷ 12 = 42

From (1)
1 BC + 15 u = 1640 

From (3)
Mass of the briefcase
= 1640 - 15 u
= 1640 - (15 x 42)
= 1640 - 630
= 1010 g

1010 g = 1010 ÷ 1000 = 1.01 kg

Answer(s): 1.01 kg