Box T and Box U are identical. ⁴₅ of Box T and ³₈ of Box U are filled with sand. The mass of Box U with its contents is ⁸₉ the mass of Box T with its contents. The total mass of the two boxes with their contents is 578 kg. Find the mass of an empty box.
Mass of Box T and its contents = 9 u
Mass of Box U and its contents = 8 u

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

17 u = 578 

1 u = 578 ÷ 17 = 34

Mass of Box T with its concents more than mass of Box U with its contents
= 9 u - 8 u
= 1 u
= 1 x 34
= 34 kg

Fraction of the sand that Box T had more than Box U
= ⁴₅ - ³₈
= ³²₄₀ - ¹⁵₄₀
= ¹⁷₄₀

¹⁷₄₀ of the capacity of sand in a box → 34
¹₄₀ of the capacity of sand in a box → 34 ÷ 17 = 2
¹⁵₄₀ of the capacity of sand in a box → 15 x 2 = 30 

Mass of the sand and Box U
= 8 u
= 8 x 34
= 272 kg

Mass of the empty box
= 272 - 30
= 242 kg

Answer(s): 242 kg