A briefcase with 2 books in it has a mass of 1.822 kg. When 5 more books and 11 magazines are added, the mass becomes 2.62 kg. Each book has a mass 2 times as much as each magazine. Find the mass of the briefcase when it is empty. Express the answer in kg.
1 kg = 1000 g
1.822 kg = 1.822 x 1000 = 1822 g
2.62 kg = 2.62 x 1000 = 2620 g

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

Let 1 briefcase be 1 BC.
Let 1 book be 1 B.
Let 1 magazine be 1 M.

Change the books and the magazines into units.

1 M = 1 u
1 B = 2 u

1 BC + 2 B = 1822 --- (1)

1 BC + 7 B + 11 M = 2620 --- (2)

From (1)
1 BC + 4 u = 1822 --- (3)

From (2)
1 BC + 14 u + 11 u = 2620
1 BC + 25 u = 2620 --- (4)

(4) - (3)
25 u - 4 u = 2620 - 1822
21 u = 798 

1 u = 798 ÷ 21 = 38

From (1)
1 BC + 4 u = 1822 

From (3)
Mass of the briefcase
= 1822 - 4 u
= 1822 - (4 x 38)
= 1822 - 152
= 1670 g

1670 g = 1670 ÷ 1000 = 1.67 kg

Answer(s): 1.67 kg