Box M and Box N are identical. ⁷₈ of Box M and ²₇ of Box N are filled with sand. The mass of Box N with its contents is ⁵₈ the mass of Box M with its contents. The total mass of the two boxes with their contents is 429 kg. Find the mass of an empty box.
Mass of Box M and its contents = 8 u
Mass of Box N and its contents = 5 u

Total mass of the two boxes with their contents
= 8 u + 5 u
= 13 u

13 u = 429 

1 u = 429 ÷ 13 = 33

Mass of Box M with its concents more than mass of Box N with its contents
= 8 u - 5 u
= 3 u
= 3 x 33
= 99 kg

Fraction of the sand that Box M had more than Box N
= ⁷₈ - ²₇
= ⁴⁹₅₆ - ¹⁶₅₆
= ³³₅₆

³³₅₆ of the capacity of sand in a box → 99
¹₅₆ of the capacity of sand in a box → 99 ÷ 33 = 3
¹⁶₅₆ of the capacity of sand in a box → 16 x 3 = 48 

Mass of the sand and Box N
= 5 u
= 5 x 33
= 165 kg

Mass of the empty box
= 165 - 48
= 117 kg

Answer(s): 117 kg