Box C and Box D are identical. ⁷₈ of Box C and ²₇ of Box D are filled with sand. The mass of Box D with its contents is ⁸₉ the mass of Box C with its contents. The total mass of the two boxes with their contents is 561 kg. Find the mass of an empty box.
Mass of Box C and its contents = 9 u
Mass of Box D and its contents = 8 u

Total mass of the two boxes with their contents
= 9 u + 8 u
= 17 u

17 u = 561 

1 u = 561 ÷ 17 = 33

Mass of Box C with its concents more than mass of Box D with its contents
= 9 u - 8 u
= 1 u
= 1 x 33
= 33 kg

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

³³₅₆ of the capacity of sand in a box → 33
¹₅₆ of the capacity of sand in a box → 33 ÷ 33 = 1
¹⁶₅₆ of the capacity of sand in a box → 16 x 1 = 16 

Mass of the sand and Box D
= 8 u
= 8 x 33
= 264 kg

Mass of the empty box
= 264 - 16
= 248 kg

Answer(s): 248 kg