Box N and Box P are identical. ⁵₆ of Box N and ³₅ of Box P are filled with sand. The mass of Box P with its contents is ⁹₁₀ the mass of Box N with its contents. The total mass of the two boxes with their contents is 931 kg. Find the mass of an empty box.
Mass of Box N and its contents = 10 u
Mass of Box P and its contents = 9 u

Total mass of the two boxes with their contents
= 10 u + 9 u
= 19 u

19 u = 931 

1 u = 931 ÷ 19 = 49

Mass of Box N with its concents more than mass of Box P with its contents
= 10 u - 9 u
= 1 u
= 1 x 49
= 49 kg

Fraction of the sand that Box N had more than Box P
= ⁵₆ - ³₅
= ²⁵₃₀ - ¹⁸₃₀
= ⁷₃₀

⁷₃₀ of the capacity of sand in a box → 49
¹₃₀ of the capacity of sand in a box → 49 ÷ 7 = 7
¹⁸₃₀ of the capacity of sand in a box → 18 x 7 = 126 

Mass of the sand and Box P
= 9 u
= 9 x 49
= 441 kg

Mass of the empty box
= 441 - 126
= 315 kg

Answer(s): 315 kg