Box U and Box V are identical. ⁵₆ of Box U and ²₅ of Box V are filled with sand. The mass of Box V with its contents is ⁷₉ the mass of Box U with its contents. The total mass of the two boxes with their contents is 624 kg. Find the mass of an empty box.
Mass of Box U and its contents = 9 u
Mass of Box V and its contents = 7 u

Total mass of the two boxes with their contents
= 9 u + 7 u
= 16 u

16 u = 624 

1 u = 624 ÷ 16 = 39

Mass of Box U with its concents more than mass of Box V with its contents
= 9 u - 7 u
= 2 u
= 2 x 39
= 78 kg

Fraction of the sand that Box U had more than Box V
= ⁵₆ - ²₅
= ²⁵₃₀ - ¹²₃₀
= ¹³₃₀

¹³₃₀ of the capacity of sand in a box → 78
¹₃₀ of the capacity of sand in a box → 78 ÷ 13 = 6
¹²₃₀ of the capacity of sand in a box → 12 x 6 = 72 

Mass of the sand and Box V
= 7 u
= 7 x 39
= 273 kg

Mass of the empty box
= 273 - 72
= 201 kg

Answer(s): 201 kg