Box Y and Box Z are identical. ⁴₅ of Box Y and ²₇ of Box Z are filled with sand. The mass of Box Z with its contents is ⁹₁₀ the mass of Box Y with its contents. The total mass of the two boxes with their contents is 684 kg. Find the mass of an empty box.
Mass of Box Y and its contents = 10 u
Mass of Box Z and its contents = 9 u

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

19 u = 684 

1 u = 684 ÷ 19 = 36

Mass of Box Y with its concents more than mass of Box Z with its contents
= 10 u - 9 u
= 1 u
= 1 x 36
= 36 kg

Fraction of the sand that Box Y had more than Box Z
= ⁴₅ - ²₇
= ²⁸₃₅ - ¹⁰₃₅
= ¹⁸₃₅

¹⁸₃₅ of the capacity of sand in a box → 36
¹₃₅ of the capacity of sand in a box → 36 ÷ 18 = 2
¹⁰₃₅ of the capacity of sand in a box → 10 x 2 = 20 

Mass of the sand and Box Z
= 9 u
= 9 x 36
= 324 kg

Mass of the empty box
= 324 - 20
= 304 kg

Answer(s): 304 kg