A briefcase with 5 magazines in it has a mass of 1.93 kg. When 6 more magazines and 7 guide books are added, the mass becomes 3.03 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
1.93 kg = 1.93 x 1000 = 1930 g
3.03 kg = 3.03 x 1000 = 3030 g

Number of magazines in the end
= 5 + 6
= 11

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 = 1930 --- (1)

1 BC + 11 M + 7 G = 3030 --- (2)

From (1)
1 BC + 15 u = 1930 --- (3)

From (2)
1 BC + 33 u + 7 u = 3030
1 BC + 40 u = 3030 --- (4)

(4) - (3)
40 u - 15 u = 3030 - 1930
25 u = 1100 

1 u = 1100 ÷ 25 = 44

From (1)
1 BC + 15 u = 1930 

From (3)
Mass of the briefcase
= 1930 - 15 u
= 1930 - (15 x 44)
= 1930 - 660
= 1270 g

1270 g = 1270 ÷ 1000 = 1.27 kg

Answer(s): 1.27 kg